<?xml version="1.0" encoding="ascii"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
          "DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
  <title>dadi.Inference</title>
  <link rel="stylesheet" href="epydoc.css" type="text/css" />
  <script type="text/javascript" src="epydoc.js"></script>
</head>

<body bgcolor="white" text="black" link="blue" vlink="#204080"
      alink="#204080">
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
       bgcolor="#a0c0ff" cellspacing="0">
  <tr valign="middle">

  <!-- Tree link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Index link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Help link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Project homepage -->
      <th class="navbar" align="right" width="100%">
        <table border="0" cellpadding="0" cellspacing="0">
          <tr><th class="navbar" align="center"
            ><a class="navbar" target="_top" href="http://dadi.googlecode.com">dadi</a></th>
          </tr></table></th>
  </tr>
</table>
<table width="100%" cellpadding="0" cellspacing="0">
  <tr valign="top">
    <td width="100%">
      <span class="breadcrumbs">
        <a href="dadi-module.html">Package&nbsp;dadi</a> ::
        Module&nbsp;Inference
      </span>
    </td>
    <td>
      <table cellpadding="0" cellspacing="0">
        <!-- hide/show private -->
        <tr><td align="right"><span class="options">[<a href="javascript:void(0);" class="privatelink"
    onclick="toggle_private();">hide&nbsp;private</a>]</span></td></tr>
        <tr><td align="right"><span class="options"
            >[<a href="frames.html" target="_top">frames</a
            >]&nbsp;|&nbsp;<a href="dadi.Inference-pysrc.html"
            target="_top">no&nbsp;frames</a>]</span></td></tr>
      </table>
    </td>
  </tr>
</table>
<h1 class="epydoc">Source Code for <a href="dadi.Inference-module.html">Module dadi.Inference</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno">  1</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L2"></a><tt class="py-lineno">  2</tt>  <tt class="py-line"><tt class="py-docstring">Comparison and optimization of model spectra to data.</tt> </tt>
<a name="L3"></a><tt class="py-lineno">  3</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L4"></a><tt class="py-lineno">  4</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">logging</tt> </tt>
<a name="L5"></a><tt class="py-lineno">  5</tt>  <tt class="py-line"><tt id="link-0" class="py-name" targets="Variable dadi.Hessian.logger=dadi.Hessian-module.html#logger,Variable dadi.Inference.logger=dadi.Inference-module.html#logger,Variable dadi.Integration.logger=dadi.Integration-module.html#logger,Variable dadi.Numerics.logger=dadi.Numerics-module.html#logger,Variable dadi.RunInParallel.logger=dadi.RunInParallel-module.html#logger,Variable dadi.Spectrum_mod.logger=dadi.Spectrum_mod-module.html#logger"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-0', 'logger', 'link-0');">logger</a></tt> <tt class="py-op">=</tt> <tt class="py-name">logging</tt><tt class="py-op">.</tt><tt class="py-name">getLogger</tt><tt class="py-op">(</tt><tt class="py-string">'Inference'</tt><tt class="py-op">)</tt> </tt>
<a name="L6"></a><tt class="py-lineno">  6</tt>  <tt class="py-line"> </tt>
<a name="L7"></a><tt class="py-lineno">  7</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">os</tt><tt class="py-op">,</tt><tt class="py-name">sys</tt> </tt>
<a name="L8"></a><tt class="py-lineno">  8</tt>  <tt class="py-line"> </tt>
<a name="L9"></a><tt class="py-lineno">  9</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">numpy</tt> </tt>
<a name="L10"></a><tt class="py-lineno"> 10</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">numpy</tt> <tt class="py-keyword">import</tt> <tt class="py-name">logical_and</tt><tt class="py-op">,</tt> <tt class="py-name">logical_not</tt> </tt>
<a name="L11"></a><tt class="py-lineno"> 11</tt>  <tt class="py-line"> </tt>
<a name="L12"></a><tt class="py-lineno"> 12</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt id="link-1" class="py-name" targets="Package dadi=dadi-module.html"><a title="dadi" class="py-name" href="#" onclick="return doclink('link-1', 'dadi', 'link-1');">dadi</a></tt> <tt class="py-keyword">import</tt> <tt id="link-2" class="py-name" targets="Module dadi.Misc=dadi.Misc-module.html"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-2', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">,</tt> <tt id="link-3" class="py-name" targets="Module dadi.Numerics=dadi.Numerics-module.html"><a title="dadi.Numerics" class="py-name" href="#" onclick="return doclink('link-3', 'Numerics', 'link-3');">Numerics</a></tt> </tt>
<a name="L13"></a><tt class="py-lineno"> 13</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt class="py-name">special</tt> <tt class="py-keyword">import</tt> <tt class="py-name">gammaln</tt> </tt>
<a name="L14"></a><tt class="py-lineno"> 14</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt id="link-4" class="py-name" targets="Function dadi.Inference.optimize()=dadi.Inference-module.html#optimize"><a title="dadi.Inference.optimize" class="py-name" href="#" onclick="return doclink('link-4', 'optimize', 'link-4');">optimize</a></tt> </tt>
<a name="L15"></a><tt class="py-lineno"> 15</tt>  <tt class="py-line"> </tt>
<a name="L16"></a><tt class="py-lineno"> 16</tt>  <tt class="py-line"><tt class="py-comment">#: Stores thetas</tt> </tt>
<a name="L17"></a><tt class="py-lineno"> 17</tt>  <tt class="py-line"><tt id="link-5" class="py-name" targets="Variable dadi.Inference._theta_store=dadi.Inference-module.html#_theta_store"><a title="dadi.Inference._theta_store" class="py-name" href="#" onclick="return doclink('link-5', '_theta_store', 'link-5');">_theta_store</a></tt> <tt class="py-op">=</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt> </tt>
<a name="L18"></a><tt class="py-lineno"> 18</tt>  <tt class="py-line"><tt class="py-comment">#: Counts calls to object_func</tt> </tt>
<a name="L19"></a><tt class="py-lineno"> 19</tt>  <tt class="py-line"><tt id="link-6" class="py-name" targets="Variable dadi.Inference._counter=dadi.Inference-module.html#_counter"><a title="dadi.Inference._counter" class="py-name" href="#" onclick="return doclink('link-6', '_counter', 'link-6');">_counter</a></tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L20"></a><tt class="py-lineno"> 20</tt>  <tt class="py-line"><tt class="py-comment">#: Returned when object_func is passed out-of-bounds params or gets a NaN ll.</tt> </tt>
<a name="L21"></a><tt class="py-lineno"> 21</tt>  <tt class="py-line"><tt id="link-7" class="py-name" targets="Variable dadi.Inference._out_of_bounds_val=dadi.Inference-module.html#_out_of_bounds_val"><a title="dadi.Inference._out_of_bounds_val" class="py-name" href="#" onclick="return doclink('link-7', '_out_of_bounds_val', 'link-7');">_out_of_bounds_val</a></tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-number">1e8</tt> </tt>
<a name="_object_func"></a><div id="_object_func-def"><a name="L22"></a><tt class="py-lineno"> 22</tt> <a class="py-toggle" href="#" id="_object_func-toggle" onclick="return toggle('_object_func');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#_object_func">_object_func</a><tt class="py-op">(</tt><tt class="py-param">params</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">model_func</tt><tt class="py-op">,</tt> <tt class="py-param">pts</tt><tt class="py-op">,</tt>  </tt>
<a name="L23"></a><tt class="py-lineno"> 23</tt>  <tt class="py-line">                 <tt class="py-param">lower_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">upper_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt>  </tt>
<a name="L24"></a><tt class="py-lineno"> 24</tt>  <tt class="py-line">                 <tt class="py-param">verbose</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">multinom</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-param">flush_delay</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> </tt>
<a name="L25"></a><tt class="py-lineno"> 25</tt>  <tt class="py-line">                 <tt class="py-param">func_args</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-param">func_kwargs</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">ll_scale</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> </tt>
<a name="L26"></a><tt class="py-lineno"> 26</tt>  <tt class="py-line">                 <tt class="py-param">output_stream</tt><tt class="py-op">=</tt><tt class="py-name">sys</tt><tt class="py-op">.</tt><tt class="py-name">stdout</tt><tt class="py-op">,</tt> <tt class="py-param">store_thetas</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_object_func-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_object_func-expanded"><a name="L27"></a><tt class="py-lineno"> 27</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L28"></a><tt class="py-lineno"> 28</tt>  <tt class="py-line"><tt class="py-docstring">    Objective function for optimization.</tt> </tt>
<a name="L29"></a><tt class="py-lineno"> 29</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L30"></a><tt class="py-lineno"> 30</tt>  <tt class="py-line">    <tt class="py-keyword">global</tt> <tt id="link-8" class="py-name"><a title="dadi.Inference._counter" class="py-name" href="#" onclick="return doclink('link-8', '_counter', 'link-6');">_counter</a></tt> </tt>
<a name="L31"></a><tt class="py-lineno"> 31</tt>  <tt class="py-line">    <tt id="link-9" class="py-name"><a title="dadi.Inference._counter" class="py-name" href="#" onclick="return doclink('link-9', '_counter', 'link-6');">_counter</a></tt> <tt class="py-op">+=</tt> <tt class="py-number">1</tt> </tt>
<a name="L32"></a><tt class="py-lineno"> 32</tt>  <tt class="py-line"> </tt>
<a name="L33"></a><tt class="py-lineno"> 33</tt>  <tt class="py-line">    <tt class="py-comment"># Deal with fixed parameters</tt> </tt>
<a name="L34"></a><tt class="py-lineno"> 34</tt>  <tt class="py-line">    <tt class="py-name">params_up</tt> <tt class="py-op">=</tt> <tt id="link-10" class="py-name" targets="Function dadi.Inference._project_params_up()=dadi.Inference-module.html#_project_params_up"><a title="dadi.Inference._project_params_up" class="py-name" href="#" onclick="return doclink('link-10', '_project_params_up', 'link-10');">_project_params_up</a></tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L35"></a><tt class="py-lineno"> 35</tt>  <tt class="py-line"> </tt>
<a name="L36"></a><tt class="py-lineno"> 36</tt>  <tt class="py-line">    <tt class="py-comment"># Check our parameter bounds</tt> </tt>
<a name="L37"></a><tt class="py-lineno"> 37</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">lower_bound</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L38"></a><tt class="py-lineno"> 38</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">pval</tt><tt class="py-op">,</tt><tt class="py-name">bound</tt> <tt class="py-keyword">in</tt> <tt class="py-name">zip</tt><tt class="py-op">(</tt><tt class="py-name">params_up</tt><tt class="py-op">,</tt> <tt class="py-name">lower_bound</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L39"></a><tt class="py-lineno"> 39</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">bound</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt> <tt class="py-keyword">and</tt> <tt class="py-name">pval</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">bound</tt><tt class="py-op">:</tt> </tt>
<a name="L40"></a><tt class="py-lineno"> 40</tt>  <tt class="py-line">                <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt id="link-11" class="py-name"><a title="dadi.Inference._out_of_bounds_val" class="py-name" href="#" onclick="return doclink('link-11', '_out_of_bounds_val', 'link-7');">_out_of_bounds_val</a></tt><tt class="py-op">/</tt><tt class="py-name">ll_scale</tt> </tt>
<a name="L41"></a><tt class="py-lineno"> 41</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">upper_bound</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L42"></a><tt class="py-lineno"> 42</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">pval</tt><tt class="py-op">,</tt><tt class="py-name">bound</tt> <tt class="py-keyword">in</tt> <tt class="py-name">zip</tt><tt class="py-op">(</tt><tt class="py-name">params_up</tt><tt class="py-op">,</tt> <tt class="py-name">upper_bound</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L43"></a><tt class="py-lineno"> 43</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">bound</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt> <tt class="py-keyword">and</tt> <tt class="py-name">pval</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">bound</tt><tt class="py-op">:</tt> </tt>
<a name="L44"></a><tt class="py-lineno"> 44</tt>  <tt class="py-line">                <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt id="link-12" class="py-name"><a title="dadi.Inference._out_of_bounds_val" class="py-name" href="#" onclick="return doclink('link-12', '_out_of_bounds_val', 'link-7');">_out_of_bounds_val</a></tt><tt class="py-op">/</tt><tt class="py-name">ll_scale</tt> </tt>
<a name="L45"></a><tt class="py-lineno"> 45</tt>  <tt class="py-line"> </tt>
<a name="L46"></a><tt class="py-lineno"> 46</tt>  <tt class="py-line">    <tt class="py-name">ns</tt> <tt class="py-op">=</tt> <tt class="py-name">data</tt><tt class="py-op">.</tt><tt id="link-13" class="py-name" targets="Method dadi.Spectrum_mod.Spectrum.sample_sizes()=dadi.Spectrum_mod.Spectrum-class.html#sample_sizes"><a title="dadi.Spectrum_mod.Spectrum.sample_sizes" class="py-name" href="#" onclick="return doclink('link-13', 'sample_sizes', 'link-13');">sample_sizes</a></tt>  </tt>
<a name="L47"></a><tt class="py-lineno"> 47</tt>  <tt class="py-line">    <tt class="py-name">all_args</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">params_up</tt><tt class="py-op">,</tt> <tt class="py-name">ns</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">list</tt><tt class="py-op">(</tt><tt class="py-name">func_args</tt><tt class="py-op">)</tt> </tt>
<a name="L48"></a><tt class="py-lineno"> 48</tt>  <tt class="py-line">    <tt class="py-comment"># Pass the pts argument via keyword, but don't alter the passed-in </tt> </tt>
<a name="L49"></a><tt class="py-lineno"> 49</tt>  <tt class="py-line">    <tt class="py-comment"># func_kwargs</tt> </tt>
<a name="L50"></a><tt class="py-lineno"> 50</tt>  <tt class="py-line">    <tt class="py-name">func_kwargs</tt> <tt class="py-op">=</tt> <tt class="py-name">func_kwargs</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L51"></a><tt class="py-lineno"> 51</tt>  <tt class="py-line">    <tt class="py-name">func_kwargs</tt><tt class="py-op">[</tt><tt class="py-string">'pts'</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">pts</tt> </tt>
<a name="L52"></a><tt class="py-lineno"> 52</tt>  <tt class="py-line">    <tt class="py-name">sfs</tt> <tt class="py-op">=</tt> <tt class="py-name">model_func</tt><tt class="py-op">(</tt><tt class="py-op">*</tt><tt class="py-name">all_args</tt><tt class="py-op">,</tt> <tt class="py-op">**</tt><tt class="py-name">func_kwargs</tt><tt class="py-op">)</tt> </tt>
<a name="L53"></a><tt class="py-lineno"> 53</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">multinom</tt><tt class="py-op">:</tt> </tt>
<a name="L54"></a><tt class="py-lineno"> 54</tt>  <tt class="py-line">        <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt id="link-14" class="py-name" targets="Function dadi.Inference.ll_multinom()=dadi.Inference-module.html#ll_multinom"><a title="dadi.Inference.ll_multinom" class="py-name" href="#" onclick="return doclink('link-14', 'll_multinom', 'link-14');">ll_multinom</a></tt><tt class="py-op">(</tt><tt class="py-name">sfs</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
<a name="L55"></a><tt class="py-lineno"> 55</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L56"></a><tt class="py-lineno"> 56</tt>  <tt class="py-line">        <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt id="link-15" class="py-name" targets="Function dadi.Inference.ll()=dadi.Inference-module.html#ll"><a title="dadi.Inference.ll" class="py-name" href="#" onclick="return doclink('link-15', 'll', 'link-15');">ll</a></tt><tt class="py-op">(</tt><tt class="py-name">sfs</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
<a name="L57"></a><tt class="py-lineno"> 57</tt>  <tt class="py-line"> </tt>
<a name="L58"></a><tt class="py-lineno"> 58</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">store_thetas</tt><tt class="py-op">:</tt> </tt>
<a name="L59"></a><tt class="py-lineno"> 59</tt>  <tt class="py-line">        <tt class="py-keyword">global</tt> <tt id="link-16" class="py-name"><a title="dadi.Inference._theta_store" class="py-name" href="#" onclick="return doclink('link-16', '_theta_store', 'link-5');">_theta_store</a></tt> </tt>
<a name="L60"></a><tt class="py-lineno"> 60</tt>  <tt class="py-line">        <tt id="link-17" class="py-name"><a title="dadi.Inference._theta_store" class="py-name" href="#" onclick="return doclink('link-17', '_theta_store', 'link-5');">_theta_store</a></tt><tt class="py-op">[</tt><tt class="py-name">tuple</tt><tt class="py-op">(</tt><tt class="py-name">params</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt id="link-18" class="py-name" targets="Function dadi.Inference.optimal_sfs_scaling()=dadi.Inference-module.html#optimal_sfs_scaling"><a title="dadi.Inference.optimal_sfs_scaling" class="py-name" href="#" onclick="return doclink('link-18', 'optimal_sfs_scaling', 'link-18');">optimal_sfs_scaling</a></tt><tt class="py-op">(</tt><tt class="py-name">sfs</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
<a name="L61"></a><tt class="py-lineno"> 61</tt>  <tt class="py-line"> </tt>
<a name="L62"></a><tt class="py-lineno"> 62</tt>  <tt class="py-line">    <tt class="py-comment"># Bad result</tt> </tt>
<a name="L63"></a><tt class="py-lineno"> 63</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isnan</tt><tt class="py-op">(</tt><tt class="py-name">result</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L64"></a><tt class="py-lineno"> 64</tt>  <tt class="py-line">        <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt id="link-19" class="py-name"><a title="dadi.Inference._out_of_bounds_val" class="py-name" href="#" onclick="return doclink('link-19', '_out_of_bounds_val', 'link-7');">_out_of_bounds_val</a></tt> </tt>
<a name="L65"></a><tt class="py-lineno"> 65</tt>  <tt class="py-line"> </tt>
<a name="L66"></a><tt class="py-lineno"> 66</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-op">(</tt><tt class="py-name">verbose</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-op">(</tt><tt id="link-20" class="py-name"><a title="dadi.Inference._counter" class="py-name" href="#" onclick="return doclink('link-20', '_counter', 'link-6');">_counter</a></tt> <tt class="py-op">%</tt> <tt class="py-name">verbose</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L67"></a><tt class="py-lineno"> 67</tt>  <tt class="py-line">        <tt class="py-name">param_str</tt> <tt class="py-op">=</tt> <tt class="py-string">'array([%s])'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-string">', '</tt><tt class="py-op">.</tt><tt class="py-name">join</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-string">'%- 12g'</tt><tt class="py-op">%</tt><tt class="py-name">v</tt> <tt class="py-keyword">for</tt> <tt class="py-name">v</tt> <tt class="py-keyword">in</tt> <tt class="py-name">params_up</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L68"></a><tt class="py-lineno"> 68</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt><tt class="py-op">.</tt><tt class="py-name">write</tt><tt class="py-op">(</tt><tt class="py-string">'%-8i, %-12g, %s%s'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt id="link-21" class="py-name"><a title="dadi.Inference._counter" class="py-name" href="#" onclick="return doclink('link-21', '_counter', 'link-6');">_counter</a></tt><tt class="py-op">,</tt> <tt class="py-name">result</tt><tt class="py-op">,</tt> <tt class="py-name">param_str</tt><tt class="py-op">,</tt> </tt>
<a name="L69"></a><tt class="py-lineno"> 69</tt>  <tt class="py-line">                                                   <tt class="py-name">os</tt><tt class="py-op">.</tt><tt class="py-name">linesep</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L70"></a><tt class="py-lineno"> 70</tt>  <tt class="py-line">        <tt id="link-22" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-22', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-23" class="py-name" targets="Function dadi.Misc.delayed_flush()=dadi.Misc-module.html#delayed_flush"><a title="dadi.Misc.delayed_flush" class="py-name" href="#" onclick="return doclink('link-23', 'delayed_flush', 'link-23');">delayed_flush</a></tt><tt class="py-op">(</tt><tt class="py-name">delay</tt><tt class="py-op">=</tt><tt class="py-name">flush_delay</tt><tt class="py-op">)</tt> </tt>
<a name="L71"></a><tt class="py-lineno"> 71</tt>  <tt class="py-line"> </tt>
<a name="L72"></a><tt class="py-lineno"> 72</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt class="py-name">result</tt><tt class="py-op">/</tt><tt class="py-name">ll_scale</tt> </tt>
</div><a name="L73"></a><tt class="py-lineno"> 73</tt>  <tt class="py-line"> </tt>
<a name="_object_func_log"></a><div id="_object_func_log-def"><a name="L74"></a><tt class="py-lineno"> 74</tt> <a class="py-toggle" href="#" id="_object_func_log-toggle" onclick="return toggle('_object_func_log');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#_object_func_log">_object_func_log</a><tt class="py-op">(</tt><tt class="py-param">log_params</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-param">args</tt><tt class="py-op">,</tt> <tt class="py-op">**</tt><tt class="py-param">kwargs</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_object_func_log-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_object_func_log-expanded"><a name="L75"></a><tt class="py-lineno"> 75</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L76"></a><tt class="py-lineno"> 76</tt>  <tt class="py-line"><tt class="py-docstring">    Objective function for optimization in log(params).</tt> </tt>
<a name="L77"></a><tt class="py-lineno"> 77</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L78"></a><tt class="py-lineno"> 78</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-24" class="py-name" targets="Function dadi.Inference._object_func()=dadi.Inference-module.html#_object_func"><a title="dadi.Inference._object_func" class="py-name" href="#" onclick="return doclink('link-24', '_object_func', 'link-24');">_object_func</a></tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">exp</tt><tt class="py-op">(</tt><tt class="py-name">log_params</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">,</tt> <tt class="py-op">**</tt><tt class="py-name">kwargs</tt><tt class="py-op">)</tt> </tt>
</div><a name="L79"></a><tt class="py-lineno"> 79</tt>  <tt class="py-line"> </tt>
<a name="optimize_log"></a><div id="optimize_log-def"><a name="L80"></a><tt class="py-lineno"> 80</tt> <a class="py-toggle" href="#" id="optimize_log-toggle" onclick="return toggle('optimize_log');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimize_log">optimize_log</a><tt class="py-op">(</tt><tt class="py-param">p0</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">model_func</tt><tt class="py-op">,</tt> <tt class="py-param">pts</tt><tt class="py-op">,</tt> <tt class="py-param">lower_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">upper_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> </tt>
<a name="L81"></a><tt class="py-lineno"> 81</tt>  <tt class="py-line">                 <tt class="py-param">verbose</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">flush_delay</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">epsilon</tt><tt class="py-op">=</tt><tt class="py-number">1e-3</tt><tt class="py-op">,</tt>  </tt>
<a name="L82"></a><tt class="py-lineno"> 82</tt>  <tt class="py-line">                 <tt class="py-param">gtol</tt><tt class="py-op">=</tt><tt class="py-number">1e-5</tt><tt class="py-op">,</tt> <tt class="py-param">multinom</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-param">maxiter</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">full_output</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L83"></a><tt class="py-lineno"> 83</tt>  <tt class="py-line">                 <tt class="py-param">func_args</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-param">func_kwargs</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">ll_scale</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> </tt>
<a name="L84"></a><tt class="py-lineno"> 84</tt>  <tt class="py-line">                 <tt class="py-param">output_file</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimize_log-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimize_log-expanded"><a name="L85"></a><tt class="py-lineno"> 85</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L86"></a><tt class="py-lineno"> 86</tt>  <tt class="py-line"><tt class="py-docstring">    Optimize log(params) to fit model to data using the BFGS method.</tt> </tt>
<a name="L87"></a><tt class="py-lineno"> 87</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L88"></a><tt class="py-lineno"> 88</tt>  <tt class="py-line"><tt class="py-docstring">    This optimization method works well when we start reasonably close to the</tt> </tt>
<a name="L89"></a><tt class="py-lineno"> 89</tt>  <tt class="py-line"><tt class="py-docstring">    optimum. It is best at burrowing down a single minimum.</tt> </tt>
<a name="L90"></a><tt class="py-lineno"> 90</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L91"></a><tt class="py-lineno"> 91</tt>  <tt class="py-line"><tt class="py-docstring">    Because this works in log(params), it cannot explore values of params &lt; 0.</tt> </tt>
<a name="L92"></a><tt class="py-lineno"> 92</tt>  <tt class="py-line"><tt class="py-docstring">    It should also perform better when parameters range over scales.</tt> </tt>
<a name="L93"></a><tt class="py-lineno"> 93</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L94"></a><tt class="py-lineno"> 94</tt>  <tt class="py-line"><tt class="py-docstring">    p0: Initial parameters.</tt> </tt>
<a name="L95"></a><tt class="py-lineno"> 95</tt>  <tt class="py-line"><tt class="py-docstring">    data: Spectrum with data.</tt> </tt>
<a name="L96"></a><tt class="py-lineno"> 96</tt>  <tt class="py-line"><tt class="py-docstring">    model_function: Function to evaluate model spectrum. Should take arguments</tt> </tt>
<a name="L97"></a><tt class="py-lineno"> 97</tt>  <tt class="py-line"><tt class="py-docstring">                    (params, (n1,n2...), pts)</tt> </tt>
<a name="L98"></a><tt class="py-lineno"> 98</tt>  <tt class="py-line"><tt class="py-docstring">    lower_bound: Lower bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L99"></a><tt class="py-lineno"> 99</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0.</tt> </tt>
<a name="L100"></a><tt class="py-lineno">100</tt>  <tt class="py-line"><tt class="py-docstring">    upper_bound: Upper bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L101"></a><tt class="py-lineno">101</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0.</tt> </tt>
<a name="L102"></a><tt class="py-lineno">102</tt>  <tt class="py-line"><tt class="py-docstring">    verbose: If &gt; 0, print optimization status every &lt;verbose&gt; steps.</tt> </tt>
<a name="L103"></a><tt class="py-lineno">103</tt>  <tt class="py-line"><tt class="py-docstring">    output_file: Stream verbose output into this filename. If None, stream to</tt> </tt>
<a name="L104"></a><tt class="py-lineno">104</tt>  <tt class="py-line"><tt class="py-docstring">                 standard out.</tt> </tt>
<a name="L105"></a><tt class="py-lineno">105</tt>  <tt class="py-line"><tt class="py-docstring">    flush_delay: Standard output will be flushed once every &lt;flush_delay&gt;</tt> </tt>
<a name="L106"></a><tt class="py-lineno">106</tt>  <tt class="py-line"><tt class="py-docstring">                 minutes. This is useful to avoid overloading I/O on clusters.</tt> </tt>
<a name="L107"></a><tt class="py-lineno">107</tt>  <tt class="py-line"><tt class="py-docstring">    epsilon: Step-size to use for finite-difference derivatives.</tt> </tt>
<a name="L108"></a><tt class="py-lineno">108</tt>  <tt class="py-line"><tt class="py-docstring">    gtol: Convergence criterion for optimization. For more info, </tt> </tt>
<a name="L109"></a><tt class="py-lineno">109</tt>  <tt class="py-line"><tt class="py-docstring">          see help(scipy.optimize.fmin_bfgs)</tt> </tt>
<a name="L110"></a><tt class="py-lineno">110</tt>  <tt class="py-line"><tt class="py-docstring">    multinom: If True, do a multinomial fit where model is optimially scaled to</tt> </tt>
<a name="L111"></a><tt class="py-lineno">111</tt>  <tt class="py-line"><tt class="py-docstring">              data at each step. If False, assume theta is a parameter and do</tt> </tt>
<a name="L112"></a><tt class="py-lineno">112</tt>  <tt class="py-line"><tt class="py-docstring">              no scaling.</tt> </tt>
<a name="L113"></a><tt class="py-lineno">113</tt>  <tt class="py-line"><tt class="py-docstring">    maxiter: Maximum iterations to run for.</tt> </tt>
<a name="L114"></a><tt class="py-lineno">114</tt>  <tt class="py-line"><tt class="py-docstring">    full_output: If True, return full outputs as in described in </tt> </tt>
<a name="L115"></a><tt class="py-lineno">115</tt>  <tt class="py-line"><tt class="py-docstring">                 help(scipy.optimize.fmin_bfgs)</tt> </tt>
<a name="L116"></a><tt class="py-lineno">116</tt>  <tt class="py-line"><tt class="py-docstring">    func_args: Additional arguments to model_func. It is assumed that </tt> </tt>
<a name="L117"></a><tt class="py-lineno">117</tt>  <tt class="py-line"><tt class="py-docstring">               model_func's first argument is an array of parameters to</tt> </tt>
<a name="L118"></a><tt class="py-lineno">118</tt>  <tt class="py-line"><tt class="py-docstring">               optimize, that its second argument is an array of sample sizes</tt> </tt>
<a name="L119"></a><tt class="py-lineno">119</tt>  <tt class="py-line"><tt class="py-docstring">               for the sfs, and that its last argument is the list of grid</tt> </tt>
<a name="L120"></a><tt class="py-lineno">120</tt>  <tt class="py-line"><tt class="py-docstring">               points to use in evaluation.</tt> </tt>
<a name="L121"></a><tt class="py-lineno">121</tt>  <tt class="py-line"><tt class="py-docstring">               Using func_args.</tt> </tt>
<a name="L122"></a><tt class="py-lineno">122</tt>  <tt class="py-line"><tt class="py-docstring">               For example, you could define your model function as</tt> </tt>
<a name="L123"></a><tt class="py-lineno">123</tt>  <tt class="py-line"><tt class="py-docstring">               def func((p1,p2), ns, f1, f2, pts):</tt> </tt>
<a name="L124"></a><tt class="py-lineno">124</tt>  <tt class="py-line"><tt class="py-docstring">                   ....</tt> </tt>
<a name="L125"></a><tt class="py-lineno">125</tt>  <tt class="py-line"><tt class="py-docstring">               If you wanted to fix f1=0.1 and f2=0.2 in the optimization, you</tt> </tt>
<a name="L126"></a><tt class="py-lineno">126</tt>  <tt class="py-line"><tt class="py-docstring">               would pass func_args = [0.1,0.2] (and ignore the fixed_params </tt> </tt>
<a name="L127"></a><tt class="py-lineno">127</tt>  <tt class="py-line"><tt class="py-docstring">               argument).</tt> </tt>
<a name="L128"></a><tt class="py-lineno">128</tt>  <tt class="py-line"><tt class="py-docstring">    func_kwargs: Additional keyword arguments to model_func.</tt> </tt>
<a name="L129"></a><tt class="py-lineno">129</tt>  <tt class="py-line"><tt class="py-docstring">    fixed_params: If not None, should be a list used to fix model parameters at</tt> </tt>
<a name="L130"></a><tt class="py-lineno">130</tt>  <tt class="py-line"><tt class="py-docstring">                  particular values. For example, if the model parameters</tt> </tt>
<a name="L131"></a><tt class="py-lineno">131</tt>  <tt class="py-line"><tt class="py-docstring">                  are (nu1,nu2,T,m), then fixed_params = [0.5,None,None,2]</tt> </tt>
<a name="L132"></a><tt class="py-lineno">132</tt>  <tt class="py-line"><tt class="py-docstring">                  will hold nu1=0.5 and m=2. The optimizer will only change </tt> </tt>
<a name="L133"></a><tt class="py-lineno">133</tt>  <tt class="py-line"><tt class="py-docstring">                  T and m. Note that the bounds lists must include all</tt> </tt>
<a name="L134"></a><tt class="py-lineno">134</tt>  <tt class="py-line"><tt class="py-docstring">                  parameters. Optimization will fail if the fixed values</tt> </tt>
<a name="L135"></a><tt class="py-lineno">135</tt>  <tt class="py-line"><tt class="py-docstring">                  lie outside their bounds. A full-length p0 should be passed</tt> </tt>
<a name="L136"></a><tt class="py-lineno">136</tt>  <tt class="py-line"><tt class="py-docstring">                  in; values corresponding to fixed parameters are ignored.</tt> </tt>
<a name="L137"></a><tt class="py-lineno">137</tt>  <tt class="py-line"><tt class="py-docstring">                  For example, suppose your model function is </tt> </tt>
<a name="L138"></a><tt class="py-lineno">138</tt>  <tt class="py-line"><tt class="py-docstring">                  def func((p1,f1,p2,f2), ns, pts):</tt> </tt>
<a name="L139"></a><tt class="py-lineno">139</tt>  <tt class="py-line"><tt class="py-docstring">                      ....</tt> </tt>
<a name="L140"></a><tt class="py-lineno">140</tt>  <tt class="py-line"><tt class="py-docstring">                  If you wanted to fix f1=0.1 and f2=0.2 in the optimization, </tt> </tt>
<a name="L141"></a><tt class="py-lineno">141</tt>  <tt class="py-line"><tt class="py-docstring">                  you would pass fixed_params = [None,0.1,None,0.2] (and ignore</tt> </tt>
<a name="L142"></a><tt class="py-lineno">142</tt>  <tt class="py-line"><tt class="py-docstring">                  the func_args argument).</tt> </tt>
<a name="L143"></a><tt class="py-lineno">143</tt>  <tt class="py-line"><tt class="py-docstring">    ll_scale: The bfgs algorithm may fail if your initial log-likelihood is</tt> </tt>
<a name="L144"></a><tt class="py-lineno">144</tt>  <tt class="py-line"><tt class="py-docstring">              too large. (This appears to be a flaw in the scipy</tt> </tt>
<a name="L145"></a><tt class="py-lineno">145</tt>  <tt class="py-line"><tt class="py-docstring">              implementation.) To overcome this, pass ll_scale &gt; 1, which will</tt> </tt>
<a name="L146"></a><tt class="py-lineno">146</tt>  <tt class="py-line"><tt class="py-docstring">              simply reduce the magnitude of the log-likelihood. Once in a</tt> </tt>
<a name="L147"></a><tt class="py-lineno">147</tt>  <tt class="py-line"><tt class="py-docstring">              region of reasonable likelihood, you'll probably want to</tt> </tt>
<a name="L148"></a><tt class="py-lineno">148</tt>  <tt class="py-line"><tt class="py-docstring">              re-optimize with ll_scale=1.</tt> </tt>
<a name="L149"></a><tt class="py-lineno">149</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L150"></a><tt class="py-lineno">150</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L151"></a><tt class="py-lineno">151</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">file</tt><tt class="py-op">(</tt><tt class="py-name">output_file</tt><tt class="py-op">,</tt> <tt class="py-string">'w'</tt><tt class="py-op">)</tt> </tt>
<a name="L152"></a><tt class="py-lineno">152</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L153"></a><tt class="py-lineno">153</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">sys</tt><tt class="py-op">.</tt><tt class="py-name">stdout</tt> </tt>
<a name="L154"></a><tt class="py-lineno">154</tt>  <tt class="py-line"> </tt>
<a name="L155"></a><tt class="py-lineno">155</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">,</tt> <tt class="py-name">model_func</tt><tt class="py-op">,</tt> <tt class="py-name">pts</tt><tt class="py-op">,</tt> <tt class="py-name">lower_bound</tt><tt class="py-op">,</tt> <tt class="py-name">upper_bound</tt><tt class="py-op">,</tt> <tt class="py-name">verbose</tt><tt class="py-op">,</tt> </tt>
<a name="L156"></a><tt class="py-lineno">156</tt>  <tt class="py-line">            <tt class="py-name">multinom</tt><tt class="py-op">,</tt> <tt class="py-name">flush_delay</tt><tt class="py-op">,</tt> <tt class="py-name">func_args</tt><tt class="py-op">,</tt> <tt class="py-name">func_kwargs</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">,</tt>  </tt>
<a name="L157"></a><tt class="py-lineno">157</tt>  <tt class="py-line">            <tt class="py-name">ll_scale</tt><tt class="py-op">,</tt> <tt class="py-name">output_stream</tt><tt class="py-op">)</tt> </tt>
<a name="L158"></a><tt class="py-lineno">158</tt>  <tt class="py-line"> </tt>
<a name="L159"></a><tt class="py-lineno">159</tt>  <tt class="py-line">    <tt class="py-name">p0</tt> <tt class="py-op">=</tt> <tt id="link-25" class="py-name" targets="Function dadi.Inference._project_params_down()=dadi.Inference-module.html#_project_params_down"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-25', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L160"></a><tt class="py-lineno">160</tt>  <tt class="py-line">    <tt class="py-name">outputs</tt> <tt class="py-op">=</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt id="link-26" class="py-name"><a title="dadi.Inference.optimize" class="py-name" href="#" onclick="return doclink('link-26', 'optimize', 'link-4');">optimize</a></tt><tt class="py-op">.</tt><tt class="py-name">fmin_bfgs</tt><tt class="py-op">(</tt><tt id="link-27" class="py-name" targets="Function dadi.Inference._object_func_log()=dadi.Inference-module.html#_object_func_log"><a title="dadi.Inference._object_func_log" class="py-name" href="#" onclick="return doclink('link-27', '_object_func_log', 'link-27');">_object_func_log</a></tt><tt class="py-op">,</tt>  </tt>
<a name="L161"></a><tt class="py-lineno">161</tt>  <tt class="py-line">                                       <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">log</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">epsilon</tt><tt class="py-op">=</tt><tt class="py-name">epsilon</tt><tt class="py-op">,</tt> </tt>
<a name="L162"></a><tt class="py-lineno">162</tt>  <tt class="py-line">                                       <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">args</tt><tt class="py-op">,</tt> <tt class="py-name">gtol</tt><tt class="py-op">=</tt><tt class="py-name">gtol</tt><tt class="py-op">,</tt>  </tt>
<a name="L163"></a><tt class="py-lineno">163</tt>  <tt class="py-line">                                       <tt class="py-name">full_output</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> </tt>
<a name="L164"></a><tt class="py-lineno">164</tt>  <tt class="py-line">                                       <tt class="py-name">disp</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L165"></a><tt class="py-lineno">165</tt>  <tt class="py-line">                                       <tt class="py-name">maxiter</tt><tt class="py-op">=</tt><tt class="py-name">maxiter</tt><tt class="py-op">)</tt> </tt>
<a name="L166"></a><tt class="py-lineno">166</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">gopt</tt><tt class="py-op">,</tt> <tt class="py-name">Bopt</tt><tt class="py-op">,</tt> <tt class="py-name">func_calls</tt><tt class="py-op">,</tt> <tt class="py-name">grad_calls</tt><tt class="py-op">,</tt> <tt class="py-name">warnflag</tt> <tt class="py-op">=</tt> <tt class="py-name">outputs</tt> </tt>
<a name="L167"></a><tt class="py-lineno">167</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt> <tt class="py-op">=</tt> <tt id="link-28" class="py-name"><a title="dadi.Inference._project_params_up" class="py-name" href="#" onclick="return doclink('link-28', '_project_params_up', 'link-10');">_project_params_up</a></tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">exp</tt><tt class="py-op">(</tt><tt class="py-name">xopt</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L168"></a><tt class="py-lineno">168</tt>  <tt class="py-line"> </tt>
<a name="L169"></a><tt class="py-lineno">169</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L170"></a><tt class="py-lineno">170</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt><tt class="py-op">.</tt><tt class="py-name">close</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L171"></a><tt class="py-lineno">171</tt>  <tt class="py-line"> </tt>
<a name="L172"></a><tt class="py-lineno">172</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L173"></a><tt class="py-lineno">173</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt> </tt>
<a name="L174"></a><tt class="py-lineno">174</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L175"></a><tt class="py-lineno">175</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">gopt</tt><tt class="py-op">,</tt> <tt class="py-name">Bopt</tt><tt class="py-op">,</tt> <tt class="py-name">func_calls</tt><tt class="py-op">,</tt> <tt class="py-name">grad_calls</tt><tt class="py-op">,</tt> <tt class="py-name">warnflag</tt> </tt>
</div><a name="L176"></a><tt class="py-lineno">176</tt>  <tt class="py-line"> </tt>
<a name="optimize_log_lbfgsb"></a><div id="optimize_log_lbfgsb-def"><a name="L177"></a><tt class="py-lineno">177</tt> <a class="py-toggle" href="#" id="optimize_log_lbfgsb-toggle" onclick="return toggle('optimize_log_lbfgsb');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimize_log_lbfgsb">optimize_log_lbfgsb</a><tt class="py-op">(</tt><tt class="py-param">p0</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">model_func</tt><tt class="py-op">,</tt> <tt class="py-param">pts</tt><tt class="py-op">,</tt>  </tt>
<a name="L178"></a><tt class="py-lineno">178</tt>  <tt class="py-line">                        <tt class="py-param">lower_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">upper_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> </tt>
<a name="L179"></a><tt class="py-lineno">179</tt>  <tt class="py-line">                        <tt class="py-param">verbose</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">flush_delay</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">epsilon</tt><tt class="py-op">=</tt><tt class="py-number">1e-3</tt><tt class="py-op">,</tt>  </tt>
<a name="L180"></a><tt class="py-lineno">180</tt>  <tt class="py-line">                        <tt class="py-param">pgtol</tt><tt class="py-op">=</tt><tt class="py-number">1e-5</tt><tt class="py-op">,</tt> <tt class="py-param">multinom</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-param">maxiter</tt><tt class="py-op">=</tt><tt class="py-number">1e5</tt><tt class="py-op">,</tt>  </tt>
<a name="L181"></a><tt class="py-lineno">181</tt>  <tt class="py-line">                        <tt class="py-param">full_output</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L182"></a><tt class="py-lineno">182</tt>  <tt class="py-line">                        <tt class="py-param">func_args</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-param">func_kwargs</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt>  </tt>
<a name="L183"></a><tt class="py-lineno">183</tt>  <tt class="py-line">                        <tt class="py-param">ll_scale</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">output_file</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimize_log_lbfgsb-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimize_log_lbfgsb-expanded"><a name="L184"></a><tt class="py-lineno">184</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L185"></a><tt class="py-lineno">185</tt>  <tt class="py-line"><tt class="py-docstring">    Optimize log(params) to fit model to data using the L-BFGS-B method.</tt> </tt>
<a name="L186"></a><tt class="py-lineno">186</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L187"></a><tt class="py-lineno">187</tt>  <tt class="py-line"><tt class="py-docstring">    This optimization method works well when we start reasonably close to the</tt> </tt>
<a name="L188"></a><tt class="py-lineno">188</tt>  <tt class="py-line"><tt class="py-docstring">    optimum. It is best at burrowing down a single minimum. This method is</tt> </tt>
<a name="L189"></a><tt class="py-lineno">189</tt>  <tt class="py-line"><tt class="py-docstring">    better than optimize_log if the optimum lies at one or more of the</tt> </tt>
<a name="L190"></a><tt class="py-lineno">190</tt>  <tt class="py-line"><tt class="py-docstring">    parameter bounds. However, if your optimum is not on the bounds, this</tt> </tt>
<a name="L191"></a><tt class="py-lineno">191</tt>  <tt class="py-line"><tt class="py-docstring">    method may be much slower.</tt> </tt>
<a name="L192"></a><tt class="py-lineno">192</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L193"></a><tt class="py-lineno">193</tt>  <tt class="py-line"><tt class="py-docstring">    Because this works in log(params), it cannot explore values of params &lt; 0.</tt> </tt>
<a name="L194"></a><tt class="py-lineno">194</tt>  <tt class="py-line"><tt class="py-docstring">    It should also perform better when parameters range over scales.</tt> </tt>
<a name="L195"></a><tt class="py-lineno">195</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L196"></a><tt class="py-lineno">196</tt>  <tt class="py-line"><tt class="py-docstring">    p0: Initial parameters.</tt> </tt>
<a name="L197"></a><tt class="py-lineno">197</tt>  <tt class="py-line"><tt class="py-docstring">    data: Spectrum with data.</tt> </tt>
<a name="L198"></a><tt class="py-lineno">198</tt>  <tt class="py-line"><tt class="py-docstring">    model_function: Function to evaluate model spectrum. Should take arguments</tt> </tt>
<a name="L199"></a><tt class="py-lineno">199</tt>  <tt class="py-line"><tt class="py-docstring">                    (params, (n1,n2...), pts)</tt> </tt>
<a name="L200"></a><tt class="py-lineno">200</tt>  <tt class="py-line"><tt class="py-docstring">    lower_bound: Lower bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L201"></a><tt class="py-lineno">201</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0. A parameter can be declared unbound by assigning</tt> </tt>
<a name="L202"></a><tt class="py-lineno">202</tt>  <tt class="py-line"><tt class="py-docstring">                 a bound of None.</tt> </tt>
<a name="L203"></a><tt class="py-lineno">203</tt>  <tt class="py-line"><tt class="py-docstring">    upper_bound: Upper bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L204"></a><tt class="py-lineno">204</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0. A parameter can be declared unbound by assigning</tt> </tt>
<a name="L205"></a><tt class="py-lineno">205</tt>  <tt class="py-line"><tt class="py-docstring">                 a bound of None.</tt> </tt>
<a name="L206"></a><tt class="py-lineno">206</tt>  <tt class="py-line"><tt class="py-docstring">    verbose: If &gt; 0, print optimization status every &lt;verbose&gt; steps.</tt> </tt>
<a name="L207"></a><tt class="py-lineno">207</tt>  <tt class="py-line"><tt class="py-docstring">    output_file: Stream verbose output into this filename. If None, stream to</tt> </tt>
<a name="L208"></a><tt class="py-lineno">208</tt>  <tt class="py-line"><tt class="py-docstring">                 standard out.</tt> </tt>
<a name="L209"></a><tt class="py-lineno">209</tt>  <tt class="py-line"><tt class="py-docstring">    flush_delay: Standard output will be flushed once every &lt;flush_delay&gt;</tt> </tt>
<a name="L210"></a><tt class="py-lineno">210</tt>  <tt class="py-line"><tt class="py-docstring">                 minutes. This is useful to avoid overloading I/O on clusters.</tt> </tt>
<a name="L211"></a><tt class="py-lineno">211</tt>  <tt class="py-line"><tt class="py-docstring">    epsilon: Step-size to use for finite-difference derivatives.</tt> </tt>
<a name="L212"></a><tt class="py-lineno">212</tt>  <tt class="py-line"><tt class="py-docstring">    pgtol: Convergence criterion for optimization. For more info, </tt> </tt>
<a name="L213"></a><tt class="py-lineno">213</tt>  <tt class="py-line"><tt class="py-docstring">          see help(scipy.optimize.fmin_l_bfgs_b)</tt> </tt>
<a name="L214"></a><tt class="py-lineno">214</tt>  <tt class="py-line"><tt class="py-docstring">    multinom: If True, do a multinomial fit where model is optimially scaled to</tt> </tt>
<a name="L215"></a><tt class="py-lineno">215</tt>  <tt class="py-line"><tt class="py-docstring">              data at each step. If False, assume theta is a parameter and do</tt> </tt>
<a name="L216"></a><tt class="py-lineno">216</tt>  <tt class="py-line"><tt class="py-docstring">              no scaling.</tt> </tt>
<a name="L217"></a><tt class="py-lineno">217</tt>  <tt class="py-line"><tt class="py-docstring">    maxiter: Maximum algorithm iterations to run.</tt> </tt>
<a name="L218"></a><tt class="py-lineno">218</tt>  <tt class="py-line"><tt class="py-docstring">    full_output: If True, return full outputs as in described in </tt> </tt>
<a name="L219"></a><tt class="py-lineno">219</tt>  <tt class="py-line"><tt class="py-docstring">                 help(scipy.optimize.fmin_bfgs)</tt> </tt>
<a name="L220"></a><tt class="py-lineno">220</tt>  <tt class="py-line"><tt class="py-docstring">    func_args: Additional arguments to model_func. It is assumed that </tt> </tt>
<a name="L221"></a><tt class="py-lineno">221</tt>  <tt class="py-line"><tt class="py-docstring">               model_func's first argument is an array of parameters to</tt> </tt>
<a name="L222"></a><tt class="py-lineno">222</tt>  <tt class="py-line"><tt class="py-docstring">               optimize, that its second argument is an array of sample sizes</tt> </tt>
<a name="L223"></a><tt class="py-lineno">223</tt>  <tt class="py-line"><tt class="py-docstring">               for the sfs, and that its last argument is the list of grid</tt> </tt>
<a name="L224"></a><tt class="py-lineno">224</tt>  <tt class="py-line"><tt class="py-docstring">               points to use in evaluation.</tt> </tt>
<a name="L225"></a><tt class="py-lineno">225</tt>  <tt class="py-line"><tt class="py-docstring">    func_kwargs: Additional keyword arguments to model_func.</tt> </tt>
<a name="L226"></a><tt class="py-lineno">226</tt>  <tt class="py-line"><tt class="py-docstring">    fixed_params: If not None, should be a list used to fix model parameters at</tt> </tt>
<a name="L227"></a><tt class="py-lineno">227</tt>  <tt class="py-line"><tt class="py-docstring">                  particular values. For example, if the model parameters</tt> </tt>
<a name="L228"></a><tt class="py-lineno">228</tt>  <tt class="py-line"><tt class="py-docstring">                  are (nu1,nu2,T,m), then fixed_params = [0.5,None,None,2]</tt> </tt>
<a name="L229"></a><tt class="py-lineno">229</tt>  <tt class="py-line"><tt class="py-docstring">                  will hold nu1=0.5 and m=2. The optimizer will only change </tt> </tt>
<a name="L230"></a><tt class="py-lineno">230</tt>  <tt class="py-line"><tt class="py-docstring">                  T and m. Note that the bounds lists must include all</tt> </tt>
<a name="L231"></a><tt class="py-lineno">231</tt>  <tt class="py-line"><tt class="py-docstring">                  parameters. Optimization will fail if the fixed values</tt> </tt>
<a name="L232"></a><tt class="py-lineno">232</tt>  <tt class="py-line"><tt class="py-docstring">                  lie outside their bounds. A full-length p0 should be passed</tt> </tt>
<a name="L233"></a><tt class="py-lineno">233</tt>  <tt class="py-line"><tt class="py-docstring">                  in; values corresponding to fixed parameters are ignored.</tt> </tt>
<a name="L234"></a><tt class="py-lineno">234</tt>  <tt class="py-line"><tt class="py-docstring">    (See help(dadi.Inference.optimize_log for examples of func_args and </tt> </tt>
<a name="L235"></a><tt class="py-lineno">235</tt>  <tt class="py-line"><tt class="py-docstring">     fixed_params usage.)</tt> </tt>
<a name="L236"></a><tt class="py-lineno">236</tt>  <tt class="py-line"><tt class="py-docstring">    ll_scale: The bfgs algorithm may fail if your initial log-likelihood is</tt> </tt>
<a name="L237"></a><tt class="py-lineno">237</tt>  <tt class="py-line"><tt class="py-docstring">              too large. (This appears to be a flaw in the scipy</tt> </tt>
<a name="L238"></a><tt class="py-lineno">238</tt>  <tt class="py-line"><tt class="py-docstring">              implementation.) To overcome this, pass ll_scale &gt; 1, which will</tt> </tt>
<a name="L239"></a><tt class="py-lineno">239</tt>  <tt class="py-line"><tt class="py-docstring">              simply reduce the magnitude of the log-likelihood. Once in a</tt> </tt>
<a name="L240"></a><tt class="py-lineno">240</tt>  <tt class="py-line"><tt class="py-docstring">              region of reasonable likelihood, you'll probably want to</tt> </tt>
<a name="L241"></a><tt class="py-lineno">241</tt>  <tt class="py-line"><tt class="py-docstring">              re-optimize with ll_scale=1.</tt> </tt>
<a name="L242"></a><tt class="py-lineno">242</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L243"></a><tt class="py-lineno">243</tt>  <tt class="py-line"><tt class="py-docstring">    The L-BFGS-B method was developed by Ciyou Zhu, Richard Byrd, and Jorge</tt> </tt>
<a name="L244"></a><tt class="py-lineno">244</tt>  <tt class="py-line"><tt class="py-docstring">    Nocedal. The algorithm is described in:</tt> </tt>
<a name="L245"></a><tt class="py-lineno">245</tt>  <tt class="py-line"><tt class="py-docstring">      * R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound</tt> </tt>
<a name="L246"></a><tt class="py-lineno">246</tt>  <tt class="py-line"><tt class="py-docstring">        Constrained Optimization, (1995), SIAM Journal on Scientific and</tt> </tt>
<a name="L247"></a><tt class="py-lineno">247</tt>  <tt class="py-line"><tt class="py-docstring">        Statistical Computing , 16, 5, pp. 1190-1208.</tt> </tt>
<a name="L248"></a><tt class="py-lineno">248</tt>  <tt class="py-line"><tt class="py-docstring">      * C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B,</tt> </tt>
<a name="L249"></a><tt class="py-lineno">249</tt>  <tt class="py-line"><tt class="py-docstring">        FORTRAN routines for large scale bound constrained optimization (1997),</tt> </tt>
<a name="L250"></a><tt class="py-lineno">250</tt>  <tt class="py-line"><tt class="py-docstring">        ACM Transactions on Mathematical Software, Vol 23, Num. 4, pp. 550-560.</tt> </tt>
<a name="L251"></a><tt class="py-lineno">251</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L252"></a><tt class="py-lineno">252</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L253"></a><tt class="py-lineno">253</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L254"></a><tt class="py-lineno">254</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">file</tt><tt class="py-op">(</tt><tt class="py-name">output_file</tt><tt class="py-op">,</tt> <tt class="py-string">'w'</tt><tt class="py-op">)</tt> </tt>
<a name="L255"></a><tt class="py-lineno">255</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L256"></a><tt class="py-lineno">256</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">sys</tt><tt class="py-op">.</tt><tt class="py-name">stdout</tt> </tt>
<a name="L257"></a><tt class="py-lineno">257</tt>  <tt class="py-line"> </tt>
<a name="L258"></a><tt class="py-lineno">258</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">,</tt> <tt class="py-name">model_func</tt><tt class="py-op">,</tt> <tt class="py-name">pts</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">verbose</tt><tt class="py-op">,</tt> </tt>
<a name="L259"></a><tt class="py-lineno">259</tt>  <tt class="py-line">            <tt class="py-name">multinom</tt><tt class="py-op">,</tt> <tt class="py-name">flush_delay</tt><tt class="py-op">,</tt> <tt class="py-name">func_args</tt><tt class="py-op">,</tt> <tt class="py-name">func_kwargs</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">,</tt>  </tt>
<a name="L260"></a><tt class="py-lineno">260</tt>  <tt class="py-line">            <tt class="py-name">ll_scale</tt><tt class="py-op">,</tt> <tt class="py-name">output_stream</tt><tt class="py-op">)</tt> </tt>
<a name="L261"></a><tt class="py-lineno">261</tt>  <tt class="py-line"> </tt>
<a name="L262"></a><tt class="py-lineno">262</tt>  <tt class="py-line">    <tt class="py-comment"># Make bounds list. For this method it needs to be in terms of log params.</tt> </tt>
<a name="L263"></a><tt class="py-lineno">263</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">lower_bound</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L264"></a><tt class="py-lineno">264</tt>  <tt class="py-line">        <tt class="py-name">lower_bound</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">None</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt> </tt>
<a name="L265"></a><tt class="py-lineno">265</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L266"></a><tt class="py-lineno">266</tt>  <tt class="py-line">        <tt class="py-name">lower_bound</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">log</tt><tt class="py-op">(</tt><tt class="py-name">lower_bound</tt><tt class="py-op">)</tt> </tt>
<a name="L267"></a><tt class="py-lineno">267</tt>  <tt class="py-line">        <tt class="py-name">lower_bound</tt><tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isnan</tt><tt class="py-op">(</tt><tt class="py-name">lower_bound</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L268"></a><tt class="py-lineno">268</tt>  <tt class="py-line">    <tt class="py-name">lower_bound</tt> <tt class="py-op">=</tt> <tt id="link-29" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-29', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">lower_bound</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L269"></a><tt class="py-lineno">269</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">upper_bound</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L270"></a><tt class="py-lineno">270</tt>  <tt class="py-line">        <tt class="py-name">upper_bound</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">None</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt> </tt>
<a name="L271"></a><tt class="py-lineno">271</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L272"></a><tt class="py-lineno">272</tt>  <tt class="py-line">        <tt class="py-name">upper_bound</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">log</tt><tt class="py-op">(</tt><tt class="py-name">upper_bound</tt><tt class="py-op">)</tt> </tt>
<a name="L273"></a><tt class="py-lineno">273</tt>  <tt class="py-line">        <tt class="py-name">upper_bound</tt><tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isnan</tt><tt class="py-op">(</tt><tt class="py-name">upper_bound</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L274"></a><tt class="py-lineno">274</tt>  <tt class="py-line">    <tt class="py-name">upper_bound</tt> <tt class="py-op">=</tt> <tt id="link-30" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-30', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">upper_bound</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L275"></a><tt class="py-lineno">275</tt>  <tt class="py-line">    <tt class="py-name">bounds</tt> <tt class="py-op">=</tt> <tt class="py-name">list</tt><tt class="py-op">(</tt><tt class="py-name">zip</tt><tt class="py-op">(</tt><tt class="py-name">lower_bound</tt><tt class="py-op">,</tt><tt class="py-name">upper_bound</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L276"></a><tt class="py-lineno">276</tt>  <tt class="py-line"> </tt>
<a name="L277"></a><tt class="py-lineno">277</tt>  <tt class="py-line">    <tt class="py-name">p0</tt> <tt class="py-op">=</tt> <tt id="link-31" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-31', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L278"></a><tt class="py-lineno">278</tt>  <tt class="py-line"> </tt>
<a name="L279"></a><tt class="py-lineno">279</tt>  <tt class="py-line">    <tt class="py-name">outputs</tt> <tt class="py-op">=</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt id="link-32" class="py-name"><a title="dadi.Inference.optimize" class="py-name" href="#" onclick="return doclink('link-32', 'optimize', 'link-4');">optimize</a></tt><tt class="py-op">.</tt><tt class="py-name">fmin_l_bfgs_b</tt><tt class="py-op">(</tt><tt id="link-33" class="py-name"><a title="dadi.Inference._object_func_log" class="py-name" href="#" onclick="return doclink('link-33', '_object_func_log', 'link-27');">_object_func_log</a></tt><tt class="py-op">,</tt>  </tt>
<a name="L280"></a><tt class="py-lineno">280</tt>  <tt class="py-line">                                           <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">log</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">bounds</tt> <tt class="py-op">=</tt> <tt class="py-name">bounds</tt><tt class="py-op">,</tt> </tt>
<a name="L281"></a><tt class="py-lineno">281</tt>  <tt class="py-line">                                           <tt class="py-name">epsilon</tt><tt class="py-op">=</tt><tt class="py-name">epsilon</tt><tt class="py-op">,</tt> <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">args</tt><tt class="py-op">,</tt> </tt>
<a name="L282"></a><tt class="py-lineno">282</tt>  <tt class="py-line">                                           <tt class="py-name">iprint</tt> <tt class="py-op">=</tt> <tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-name">pgtol</tt><tt class="py-op">=</tt><tt class="py-name">pgtol</tt><tt class="py-op">,</tt> </tt>
<a name="L283"></a><tt class="py-lineno">283</tt>  <tt class="py-line">                                           <tt class="py-name">maxfun</tt><tt class="py-op">=</tt><tt class="py-name">maxiter</tt><tt class="py-op">,</tt> <tt class="py-name">approx_grad</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">)</tt> </tt>
<a name="L284"></a><tt class="py-lineno">284</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">info_dict</tt> <tt class="py-op">=</tt> <tt class="py-name">outputs</tt> </tt>
<a name="L285"></a><tt class="py-lineno">285</tt>  <tt class="py-line"> </tt>
<a name="L286"></a><tt class="py-lineno">286</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt> <tt class="py-op">=</tt> <tt id="link-34" class="py-name"><a title="dadi.Inference._project_params_up" class="py-name" href="#" onclick="return doclink('link-34', '_project_params_up', 'link-10');">_project_params_up</a></tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">exp</tt><tt class="py-op">(</tt><tt class="py-name">xopt</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L287"></a><tt class="py-lineno">287</tt>  <tt class="py-line"> </tt>
<a name="L288"></a><tt class="py-lineno">288</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L289"></a><tt class="py-lineno">289</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt><tt class="py-op">.</tt><tt class="py-name">close</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L290"></a><tt class="py-lineno">290</tt>  <tt class="py-line"> </tt>
<a name="L291"></a><tt class="py-lineno">291</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L292"></a><tt class="py-lineno">292</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt> </tt>
<a name="L293"></a><tt class="py-lineno">293</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L294"></a><tt class="py-lineno">294</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">info_dict</tt> </tt>
</div><a name="L295"></a><tt class="py-lineno">295</tt>  <tt class="py-line"> </tt>
<a name="minus_ll"></a><div id="minus_ll-def"><a name="L296"></a><tt class="py-lineno">296</tt> <a class="py-toggle" href="#" id="minus_ll-toggle" onclick="return toggle('minus_ll');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#minus_ll">minus_ll</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="minus_ll-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="minus_ll-expanded"><a name="L297"></a><tt class="py-lineno">297</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L298"></a><tt class="py-lineno">298</tt>  <tt class="py-line"><tt class="py-docstring">    The negative of the log-likelihood of the data given the model sfs.</tt> </tt>
<a name="L299"></a><tt class="py-lineno">299</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L300"></a><tt class="py-lineno">300</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt id="link-35" class="py-name"><a title="dadi.Inference.ll" class="py-name" href="#" onclick="return doclink('link-35', 'll', 'link-15');">ll</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
</div><a name="L301"></a><tt class="py-lineno">301</tt>  <tt class="py-line"> </tt>
<a name="ll"></a><div id="ll-def"><a name="L302"></a><tt class="py-lineno">302</tt> <a class="py-toggle" href="#" id="ll-toggle" onclick="return toggle('ll');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#ll">ll</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="ll-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="ll-expanded"><a name="L303"></a><tt class="py-lineno">303</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L304"></a><tt class="py-lineno">304</tt>  <tt class="py-line"><tt class="py-docstring">    The log-likelihood of the data given the model sfs.</tt> </tt>
<a name="L305"></a><tt class="py-lineno">305</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L306"></a><tt class="py-lineno">306</tt>  <tt class="py-line"><tt class="py-docstring">    Evaluate the log-likelihood of the data given the model. This is based on</tt> </tt>
<a name="L307"></a><tt class="py-lineno">307</tt>  <tt class="py-line"><tt class="py-docstring">    Poisson statistics, where the probability of observing k entries in a cell</tt> </tt>
<a name="L308"></a><tt class="py-lineno">308</tt>  <tt class="py-line"><tt class="py-docstring">    given that the mean number is given by the model is </tt> </tt>
<a name="L309"></a><tt class="py-lineno">309</tt>  <tt class="py-line"><tt class="py-docstring">    P(k) = exp(-model) * model**k / k!</tt> </tt>
<a name="L310"></a><tt class="py-lineno">310</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L311"></a><tt class="py-lineno">311</tt>  <tt class="py-line"><tt class="py-docstring">    Note: If either the model or the data is a masked array, the return ll will</tt> </tt>
<a name="L312"></a><tt class="py-lineno">312</tt>  <tt class="py-line"><tt class="py-docstring">          ignore any elements that are masked in *either* the model or the data.</tt> </tt>
<a name="L313"></a><tt class="py-lineno">313</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L314"></a><tt class="py-lineno">314</tt>  <tt class="py-line">    <tt class="py-name">ll_arr</tt> <tt class="py-op">=</tt> <tt id="link-36" class="py-name" targets="Function dadi.Inference.ll_per_bin()=dadi.Inference-module.html#ll_per_bin"><a title="dadi.Inference.ll_per_bin" class="py-name" href="#" onclick="return doclink('link-36', 'll_per_bin', 'link-36');">ll_per_bin</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
<a name="L315"></a><tt class="py-lineno">315</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">ll_arr</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L316"></a><tt class="py-lineno">316</tt>  <tt class="py-line"> </tt>
<a name="ll_per_bin"></a><div id="ll_per_bin-def"><a name="L317"></a><tt class="py-lineno">317</tt> <a class="py-toggle" href="#" id="ll_per_bin-toggle" onclick="return toggle('ll_per_bin');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#ll_per_bin">ll_per_bin</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">missing_model_cutoff</tt><tt class="py-op">=</tt><tt class="py-number">1e-6</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="ll_per_bin-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="ll_per_bin-expanded"><a name="L318"></a><tt class="py-lineno">318</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L319"></a><tt class="py-lineno">319</tt>  <tt class="py-line"><tt class="py-docstring">    The Poisson log-likelihood of each entry in the data given the model sfs.</tt> </tt>
<a name="L320"></a><tt class="py-lineno">320</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L321"></a><tt class="py-lineno">321</tt>  <tt class="py-line"><tt class="py-docstring">    missing_model_cutoff: Due to numerical issues, there may be entries in the</tt> </tt>
<a name="L322"></a><tt class="py-lineno">322</tt>  <tt class="py-line"><tt class="py-docstring">                          FS that cannot be stable calculated. If these entries</tt> </tt>
<a name="L323"></a><tt class="py-lineno">323</tt>  <tt class="py-line"><tt class="py-docstring">                          involve a fraction of the data larger than</tt> </tt>
<a name="L324"></a><tt class="py-lineno">324</tt>  <tt class="py-line"><tt class="py-docstring">                          missing_model_cutoff, a warning is printed.</tt> </tt>
<a name="L325"></a><tt class="py-lineno">325</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L326"></a><tt class="py-lineno">326</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt> <tt class="py-keyword">and</tt> <tt class="py-keyword">not</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt><tt class="py-op">:</tt> </tt>
<a name="L327"></a><tt class="py-lineno">327</tt>  <tt class="py-line">        <tt class="py-name">model</tt> <tt class="py-op">=</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt id="link-37" class="py-name" targets="Method dadi.Spectrum_mod.Spectrum.fold()=dadi.Spectrum_mod.Spectrum-class.html#fold"><a title="dadi.Spectrum_mod.Spectrum.fold" class="py-name" href="#" onclick="return doclink('link-37', 'fold', 'link-37');">fold</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L328"></a><tt class="py-lineno">328</tt>  <tt class="py-line"> </tt>
<a name="L329"></a><tt class="py-lineno">329</tt>  <tt class="py-line">    <tt class="py-name">final_missing</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L330"></a><tt class="py-lineno">330</tt>  <tt class="py-line"> </tt>
<a name="L331"></a><tt class="py-lineno">331</tt>  <tt class="py-line">    <tt class="py-name">missing</tt> <tt class="py-op">=</tt> <tt class="py-name">logical_and</tt><tt class="py-op">(</tt><tt class="py-name">model</tt> <tt class="py-op">&lt;</tt> <tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-name">logical_not</tt><tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">mask</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L332"></a><tt class="py-lineno">332</tt>  <tt class="py-line">    <tt class="py-name">missing_sum</tt> <tt class="py-op">=</tt> <tt class="py-name">data</tt><tt class="py-op">[</tt><tt class="py-name">missing</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L333"></a><tt class="py-lineno">333</tt>  <tt class="py-line">    <tt class="py-name">data_sum</tt> <tt class="py-op">=</tt> <tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L334"></a><tt class="py-lineno">334</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">/</tt><tt class="py-name">data_sum</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">missing_model_cutoff</tt><tt class="py-op">:</tt> </tt>
<a name="L335"></a><tt class="py-lineno">335</tt>  <tt class="py-line">        <tt id="link-38" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-38', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Model is &lt; 0 where data is not masked.'</tt><tt class="py-op">)</tt> </tt>
<a name="L336"></a><tt class="py-lineno">336</tt>  <tt class="py-line">        <tt id="link-39" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-39', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Number of affected entries is %i. Sum of data in those '</tt> </tt>
<a name="L337"></a><tt class="py-lineno">337</tt>  <tt class="py-line">                    <tt class="py-string">'entries is %g:'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L338"></a><tt class="py-lineno">338</tt>  <tt class="py-line"> </tt>
<a name="L339"></a><tt class="py-lineno">339</tt>  <tt class="py-line">    <tt class="py-comment"># If the data is 0, it's okay for the model to be 0. In that case the ll</tt> </tt>
<a name="L340"></a><tt class="py-lineno">340</tt>  <tt class="py-line">    <tt class="py-comment"># contribution is 0, which is fine.</tt> </tt>
<a name="L341"></a><tt class="py-lineno">341</tt>  <tt class="py-line">    <tt class="py-name">missing</tt> <tt class="py-op">=</tt> <tt class="py-name">logical_and</tt><tt class="py-op">(</tt><tt class="py-name">model</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-name">logical_and</tt><tt class="py-op">(</tt><tt class="py-name">data</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-name">logical_not</tt><tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">mask</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L342"></a><tt class="py-lineno">342</tt>  <tt class="py-line">    <tt class="py-name">missing_sum</tt> <tt class="py-op">=</tt> <tt class="py-name">data</tt><tt class="py-op">[</tt><tt class="py-name">missing</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L343"></a><tt class="py-lineno">343</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">/</tt><tt class="py-name">data_sum</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">missing_model_cutoff</tt><tt class="py-op">:</tt> </tt>
<a name="L344"></a><tt class="py-lineno">344</tt>  <tt class="py-line">        <tt id="link-40" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-40', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Model is 0 where data is neither masked nor 0.'</tt><tt class="py-op">)</tt> </tt>
<a name="L345"></a><tt class="py-lineno">345</tt>  <tt class="py-line">        <tt id="link-41" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-41', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Number of affected entries is %i. Sum of data in those '</tt> </tt>
<a name="L346"></a><tt class="py-lineno">346</tt>  <tt class="py-line">                    <tt class="py-string">'entries is %g:'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L347"></a><tt class="py-lineno">347</tt>  <tt class="py-line"> </tt>
<a name="L348"></a><tt class="py-lineno">348</tt>  <tt class="py-line">    <tt class="py-name">missing</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">logical_and</tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">.</tt><tt class="py-name">mask</tt><tt class="py-op">,</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">logical_not</tt><tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">mask</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L349"></a><tt class="py-lineno">349</tt>  <tt class="py-line">    <tt class="py-name">missing_sum</tt> <tt class="py-op">=</tt> <tt class="py-name">data</tt><tt class="py-op">[</tt><tt class="py-name">missing</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L350"></a><tt class="py-lineno">350</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">/</tt><tt class="py-name">data_sum</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">missing_model_cutoff</tt><tt class="py-op">:</tt> </tt>
<a name="L351"></a><tt class="py-lineno">351</tt>  <tt class="py-line">        <tt class="py-keyword">print</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">,</tt> <tt class="py-name">data_sum</tt> </tt>
<a name="L352"></a><tt class="py-lineno">352</tt>  <tt class="py-line">        <tt id="link-42" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-42', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Model is masked in some entries where data is not.'</tt><tt class="py-op">)</tt> </tt>
<a name="L353"></a><tt class="py-lineno">353</tt>  <tt class="py-line">        <tt id="link-43" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-43', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Number of affected entries is %i. Sum of data in those '</tt> </tt>
<a name="L354"></a><tt class="py-lineno">354</tt>  <tt class="py-line">                    <tt class="py-string">'entries is %g:'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L355"></a><tt class="py-lineno">355</tt>  <tt class="py-line"> </tt>
<a name="L356"></a><tt class="py-lineno">356</tt>  <tt class="py-line">    <tt class="py-name">missing</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">logical_and</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isnan</tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">logical_not</tt><tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">mask</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L357"></a><tt class="py-lineno">357</tt>  <tt class="py-line">    <tt class="py-name">missing_sum</tt> <tt class="py-op">=</tt> <tt class="py-name">data</tt><tt class="py-op">[</tt><tt class="py-name">missing</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L358"></a><tt class="py-lineno">358</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">/</tt><tt class="py-name">data_sum</tt> <tt class="py-op">&gt;</tt> <tt class="py-name">missing_model_cutoff</tt><tt class="py-op">:</tt> </tt>
<a name="L359"></a><tt class="py-lineno">359</tt>  <tt class="py-line">        <tt id="link-44" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-44', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Model is nan in some entries where data is not masked.'</tt><tt class="py-op">)</tt> </tt>
<a name="L360"></a><tt class="py-lineno">360</tt>  <tt class="py-line">        <tt id="link-45" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-45', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'Number of affected entries is %i. Sum of data in those '</tt> </tt>
<a name="L361"></a><tt class="py-lineno">361</tt>  <tt class="py-line">                    <tt class="py-string">'entries is %g:'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">missing</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">missing_sum</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L362"></a><tt class="py-lineno">362</tt>  <tt class="py-line"> </tt>
<a name="L363"></a><tt class="py-lineno">363</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt class="py-name">model</tt> <tt class="py-op">+</tt> <tt class="py-name">data</tt><tt class="py-op">*</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">ma</tt><tt class="py-op">.</tt><tt class="py-name">log</tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">gammaln</tt><tt class="py-op">(</tt><tt class="py-name">data</tt> <tt class="py-op">+</tt> <tt class="py-number">1.</tt><tt class="py-op">)</tt> </tt>
</div><a name="L364"></a><tt class="py-lineno">364</tt>  <tt class="py-line"> </tt>
<a name="ll_multinom_per_bin"></a><div id="ll_multinom_per_bin-def"><a name="L365"></a><tt class="py-lineno">365</tt> <a class="py-toggle" href="#" id="ll_multinom_per_bin-toggle" onclick="return toggle('ll_multinom_per_bin');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#ll_multinom_per_bin">ll_multinom_per_bin</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="ll_multinom_per_bin-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="ll_multinom_per_bin-expanded"><a name="L366"></a><tt class="py-lineno">366</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L367"></a><tt class="py-lineno">367</tt>  <tt class="py-line"><tt class="py-docstring">    Mutlinomial log-likelihood of each entry in the data given the model.</tt> </tt>
<a name="L368"></a><tt class="py-lineno">368</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L369"></a><tt class="py-lineno">369</tt>  <tt class="py-line"><tt class="py-docstring">    Scales the model sfs to have the optimal theta for comparison with the data.</tt> </tt>
<a name="L370"></a><tt class="py-lineno">370</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L371"></a><tt class="py-lineno">371</tt>  <tt class="py-line">    <tt class="py-name">theta_opt</tt> <tt class="py-op">=</tt> <tt id="link-46" class="py-name"><a title="dadi.Inference.optimal_sfs_scaling" class="py-name" href="#" onclick="return doclink('link-46', 'optimal_sfs_scaling', 'link-18');">optimal_sfs_scaling</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
<a name="L372"></a><tt class="py-lineno">372</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-47" class="py-name"><a title="dadi.Inference.ll_per_bin" class="py-name" href="#" onclick="return doclink('link-47', 'll_per_bin', 'link-36');">ll_per_bin</a></tt><tt class="py-op">(</tt><tt class="py-name">theta_opt</tt><tt class="py-op">*</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
</div><a name="L373"></a><tt class="py-lineno">373</tt>  <tt class="py-line"> </tt>
<a name="ll_multinom"></a><div id="ll_multinom-def"><a name="L374"></a><tt class="py-lineno">374</tt> <a class="py-toggle" href="#" id="ll_multinom-toggle" onclick="return toggle('ll_multinom');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#ll_multinom">ll_multinom</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="ll_multinom-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="ll_multinom-expanded"><a name="L375"></a><tt class="py-lineno">375</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L376"></a><tt class="py-lineno">376</tt>  <tt class="py-line"><tt class="py-docstring">    Log-likelihood of the data given the model, with optimal rescaling.</tt> </tt>
<a name="L377"></a><tt class="py-lineno">377</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L378"></a><tt class="py-lineno">378</tt>  <tt class="py-line"><tt class="py-docstring">    Evaluate the log-likelihood of the data given the model. This is based on</tt> </tt>
<a name="L379"></a><tt class="py-lineno">379</tt>  <tt class="py-line"><tt class="py-docstring">    Poisson statistics, where the probability of observing k entries in a cell</tt> </tt>
<a name="L380"></a><tt class="py-lineno">380</tt>  <tt class="py-line"><tt class="py-docstring">    given that the mean number is given by the model is </tt> </tt>
<a name="L381"></a><tt class="py-lineno">381</tt>  <tt class="py-line"><tt class="py-docstring">    P(k) = exp(-model) * model**k / k!</tt> </tt>
<a name="L382"></a><tt class="py-lineno">382</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L383"></a><tt class="py-lineno">383</tt>  <tt class="py-line"><tt class="py-docstring">    model is optimally scaled to maximize ll before calculation.</tt> </tt>
<a name="L384"></a><tt class="py-lineno">384</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L385"></a><tt class="py-lineno">385</tt>  <tt class="py-line"><tt class="py-docstring">    Note: If either the model or the data is a masked array, the return ll will</tt> </tt>
<a name="L386"></a><tt class="py-lineno">386</tt>  <tt class="py-line"><tt class="py-docstring">          ignore any elements that are masked in *either* the model or the data.</tt> </tt>
<a name="L387"></a><tt class="py-lineno">387</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L388"></a><tt class="py-lineno">388</tt>  <tt class="py-line">    <tt class="py-name">ll_arr</tt> <tt class="py-op">=</tt> <tt id="link-48" class="py-name" targets="Function dadi.Inference.ll_multinom_per_bin()=dadi.Inference-module.html#ll_multinom_per_bin"><a title="dadi.Inference.ll_multinom_per_bin" class="py-name" href="#" onclick="return doclink('link-48', 'll_multinom_per_bin', 'link-48');">ll_multinom_per_bin</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
<a name="L389"></a><tt class="py-lineno">389</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">ll_arr</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L390"></a><tt class="py-lineno">390</tt>  <tt class="py-line"> </tt>
<a name="minus_ll_multinom"></a><div id="minus_ll_multinom-def"><a name="L391"></a><tt class="py-lineno">391</tt> <a class="py-toggle" href="#" id="minus_ll_multinom-toggle" onclick="return toggle('minus_ll_multinom');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#minus_ll_multinom">minus_ll_multinom</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="minus_ll_multinom-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="minus_ll_multinom-expanded"><a name="L392"></a><tt class="py-lineno">392</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L393"></a><tt class="py-lineno">393</tt>  <tt class="py-line"><tt class="py-docstring">    The negative of the log-likelihood of the data given the model sfs.</tt> </tt>
<a name="L394"></a><tt class="py-lineno">394</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L395"></a><tt class="py-lineno">395</tt>  <tt class="py-line"><tt class="py-docstring">    Return a double that is -(log-likelihood)</tt> </tt>
<a name="L396"></a><tt class="py-lineno">396</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L397"></a><tt class="py-lineno">397</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt id="link-49" class="py-name"><a title="dadi.Inference.ll_multinom" class="py-name" href="#" onclick="return doclink('link-49', 'll_multinom', 'link-14');">ll_multinom</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
</div><a name="L398"></a><tt class="py-lineno">398</tt>  <tt class="py-line"> </tt>
<a name="linear_Poisson_residual"></a><div id="linear_Poisson_residual-def"><a name="L399"></a><tt class="py-lineno">399</tt> <a class="py-toggle" href="#" id="linear_Poisson_residual-toggle" onclick="return toggle('linear_Poisson_residual');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#linear_Poisson_residual">linear_Poisson_residual</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">mask</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="linear_Poisson_residual-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="linear_Poisson_residual-expanded"><a name="L400"></a><tt class="py-lineno">400</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L401"></a><tt class="py-lineno">401</tt>  <tt class="py-line"><tt class="py-docstring">    Return the Poisson residuals, (model - data)/sqrt(model), of model and data.</tt> </tt>
<a name="L402"></a><tt class="py-lineno">402</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L403"></a><tt class="py-lineno">403</tt>  <tt class="py-line"><tt class="py-docstring">    mask sets the level in model below which the returned residual array is</tt> </tt>
<a name="L404"></a><tt class="py-lineno">404</tt>  <tt class="py-line"><tt class="py-docstring">    masked. The default of 0 excludes values where the residuals are not </tt> </tt>
<a name="L405"></a><tt class="py-lineno">405</tt>  <tt class="py-line"><tt class="py-docstring">    defined.</tt> </tt>
<a name="L406"></a><tt class="py-lineno">406</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L407"></a><tt class="py-lineno">407</tt>  <tt class="py-line"><tt class="py-docstring">    In the limit that the mean of the Poisson distribution is large, these</tt> </tt>
<a name="L408"></a><tt class="py-lineno">408</tt>  <tt class="py-line"><tt class="py-docstring">    residuals are normally distributed. (If the mean is small, the Anscombe</tt> </tt>
<a name="L409"></a><tt class="py-lineno">409</tt>  <tt class="py-line"><tt class="py-docstring">    residuals are better.)</tt> </tt>
<a name="L410"></a><tt class="py-lineno">410</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L411"></a><tt class="py-lineno">411</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt> <tt class="py-keyword">and</tt> <tt class="py-keyword">not</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt><tt class="py-op">:</tt> </tt>
<a name="L412"></a><tt class="py-lineno">412</tt>  <tt class="py-line">        <tt class="py-name">model</tt> <tt class="py-op">=</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt id="link-50" class="py-name"><a title="dadi.Spectrum_mod.Spectrum.fold" class="py-name" href="#" onclick="return doclink('link-50', 'fold', 'link-37');">fold</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L413"></a><tt class="py-lineno">413</tt>  <tt class="py-line"> </tt>
<a name="L414"></a><tt class="py-lineno">414</tt>  <tt class="py-line">    <tt class="py-name">resid</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">model</tt> <tt class="py-op">-</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">ma</tt><tt class="py-op">.</tt><tt class="py-name">sqrt</tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L415"></a><tt class="py-lineno">415</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">mask</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L416"></a><tt class="py-lineno">416</tt>  <tt class="py-line">        <tt class="py-name">tomask</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">logical_and</tt><tt class="py-op">(</tt><tt class="py-name">model</tt> <tt class="py-op">&lt;=</tt> <tt class="py-name">mask</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt> <tt class="py-op">&lt;=</tt> <tt class="py-name">mask</tt><tt class="py-op">)</tt> </tt>
<a name="L417"></a><tt class="py-lineno">417</tt>  <tt class="py-line">        <tt class="py-name">resid</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">ma</tt><tt class="py-op">.</tt><tt class="py-name">masked_where</tt><tt class="py-op">(</tt><tt class="py-name">tomask</tt><tt class="py-op">,</tt> <tt class="py-name">resid</tt><tt class="py-op">)</tt> </tt>
<a name="L418"></a><tt class="py-lineno">418</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">resid</tt> </tt>
</div><a name="L419"></a><tt class="py-lineno">419</tt>  <tt class="py-line"> </tt>
<a name="Anscombe_Poisson_residual"></a><div id="Anscombe_Poisson_residual-def"><a name="L420"></a><tt class="py-lineno">420</tt> <a class="py-toggle" href="#" id="Anscombe_Poisson_residual-toggle" onclick="return toggle('Anscombe_Poisson_residual');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#Anscombe_Poisson_residual">Anscombe_Poisson_residual</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">mask</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Anscombe_Poisson_residual-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Anscombe_Poisson_residual-expanded"><a name="L421"></a><tt class="py-lineno">421</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L422"></a><tt class="py-lineno">422</tt>  <tt class="py-line"><tt class="py-docstring">    Return the Anscombe Poisson residuals between model and data.</tt> </tt>
<a name="L423"></a><tt class="py-lineno">423</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L424"></a><tt class="py-lineno">424</tt>  <tt class="py-line"><tt class="py-docstring">    mask sets the level in model below which the returned residual array is</tt> </tt>
<a name="L425"></a><tt class="py-lineno">425</tt>  <tt class="py-line"><tt class="py-docstring">    masked. This excludes very small values where the residuals are not normal.</tt> </tt>
<a name="L426"></a><tt class="py-lineno">426</tt>  <tt class="py-line"><tt class="py-docstring">    1e-2 seems to be a good default for the NIEHS human data. (model = 1e-2,</tt> </tt>
<a name="L427"></a><tt class="py-lineno">427</tt>  <tt class="py-line"><tt class="py-docstring">    data = 0, yields a residual of ~1.5.)</tt> </tt>
<a name="L428"></a><tt class="py-lineno">428</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L429"></a><tt class="py-lineno">429</tt>  <tt class="py-line"><tt class="py-docstring">    Residuals defined in this manner are more normally distributed than the</tt> </tt>
<a name="L430"></a><tt class="py-lineno">430</tt>  <tt class="py-line"><tt class="py-docstring">    linear residuals when the mean is small. See this reference below for</tt> </tt>
<a name="L431"></a><tt class="py-lineno">431</tt>  <tt class="py-line"><tt class="py-docstring">    justification: Pierce DA and Schafer DW, "Residuals in generalized linear</tt> </tt>
<a name="L432"></a><tt class="py-lineno">432</tt>  <tt class="py-line"><tt class="py-docstring">    models" Journal of the American Statistical Association, 81(396)977-986</tt> </tt>
<a name="L433"></a><tt class="py-lineno">433</tt>  <tt class="py-line"><tt class="py-docstring">    (1986).</tt> </tt>
<a name="L434"></a><tt class="py-lineno">434</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L435"></a><tt class="py-lineno">435</tt>  <tt class="py-line"><tt class="py-docstring">    Note that I tried implementing the "adjusted deviance" residuals, but they</tt> </tt>
<a name="L436"></a><tt class="py-lineno">436</tt>  <tt class="py-line"><tt class="py-docstring">    always looked very biased for the cases where the data was 0.</tt> </tt>
<a name="L437"></a><tt class="py-lineno">437</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L438"></a><tt class="py-lineno">438</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt> <tt class="py-keyword">and</tt> <tt class="py-keyword">not</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt><tt class="py-op">:</tt> </tt>
<a name="L439"></a><tt class="py-lineno">439</tt>  <tt class="py-line">        <tt class="py-name">model</tt> <tt class="py-op">=</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt id="link-51" class="py-name"><a title="dadi.Spectrum_mod.Spectrum.fold" class="py-name" href="#" onclick="return doclink('link-51', 'fold', 'link-37');">fold</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L440"></a><tt class="py-lineno">440</tt>  <tt class="py-line">    <tt class="py-comment"># Because my data have often been projected downward or averaged over many</tt> </tt>
<a name="L441"></a><tt class="py-lineno">441</tt>  <tt class="py-line">    <tt class="py-comment"># iterations, it appears better to apply the same transformation to the data</tt> </tt>
<a name="L442"></a><tt class="py-lineno">442</tt>  <tt class="py-line">    <tt class="py-comment"># and the model.</tt> </tt>
<a name="L443"></a><tt class="py-lineno">443</tt>  <tt class="py-line">    <tt class="py-comment"># For some reason data**(-1./3) results in entries in data that are zero</tt> </tt>
<a name="L444"></a><tt class="py-lineno">444</tt>  <tt class="py-line">    <tt class="py-comment"># becoming masked. Not just the result, but the data array itself. We use</tt> </tt>
<a name="L445"></a><tt class="py-lineno">445</tt>  <tt class="py-line">    <tt class="py-comment"># the power call to get around that.</tt> </tt>
<a name="L446"></a><tt class="py-lineno">446</tt>  <tt class="py-line">    <tt class="py-comment"># This seems to be a common problem, that we want to use numpy.ma functions</tt> </tt>
<a name="L447"></a><tt class="py-lineno">447</tt>  <tt class="py-line">    <tt class="py-comment"># on masked arrays, because otherwise the mask on the input itself can be</tt> </tt>
<a name="L448"></a><tt class="py-lineno">448</tt>  <tt class="py-line">    <tt class="py-comment"># changed. Subtle and annoying. If we need to create our own functions, we</tt> </tt>
<a name="L449"></a><tt class="py-lineno">449</tt>  <tt class="py-line">    <tt class="py-comment"># can use numpy.ma.core._MaskedUnaryOperation.</tt> </tt>
<a name="L450"></a><tt class="py-lineno">450</tt>  <tt class="py-line">    <tt class="py-name">datatrans</tt> <tt class="py-op">=</tt> <tt class="py-name">data</tt><tt class="py-op">**</tt><tt class="py-op">(</tt><tt class="py-number">2.</tt><tt class="py-op">/</tt><tt class="py-number">3</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">ma</tt><tt class="py-op">.</tt><tt class="py-name">power</tt><tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1.</tt><tt class="py-op">/</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">9</tt> </tt>
<a name="L451"></a><tt class="py-lineno">451</tt>  <tt class="py-line">    <tt class="py-name">modeltrans</tt> <tt class="py-op">=</tt> <tt class="py-name">model</tt><tt class="py-op">**</tt><tt class="py-op">(</tt><tt class="py-number">2.</tt><tt class="py-op">/</tt><tt class="py-number">3</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">ma</tt><tt class="py-op">.</tt><tt class="py-name">power</tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1.</tt><tt class="py-op">/</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">9</tt> </tt>
<a name="L452"></a><tt class="py-lineno">452</tt>  <tt class="py-line">    <tt class="py-name">resid</tt> <tt class="py-op">=</tt> <tt class="py-number">1.5</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-name">datatrans</tt> <tt class="py-op">-</tt> <tt class="py-name">modeltrans</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-name">model</tt><tt class="py-op">**</tt><tt class="py-op">(</tt><tt class="py-number">1.</tt><tt class="py-op">/</tt><tt class="py-number">6</tt><tt class="py-op">)</tt> </tt>
<a name="L453"></a><tt class="py-lineno">453</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">mask</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L454"></a><tt class="py-lineno">454</tt>  <tt class="py-line">        <tt class="py-name">tomask</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">logical_and</tt><tt class="py-op">(</tt><tt class="py-name">model</tt> <tt class="py-op">&lt;=</tt> <tt class="py-name">mask</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt> <tt class="py-op">&lt;=</tt> <tt class="py-name">mask</tt><tt class="py-op">)</tt> </tt>
<a name="L455"></a><tt class="py-lineno">455</tt>  <tt class="py-line">        <tt class="py-name">tomask</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">logical_or</tt><tt class="py-op">(</tt><tt class="py-name">tomask</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt> </tt>
<a name="L456"></a><tt class="py-lineno">456</tt>  <tt class="py-line">        <tt class="py-name">resid</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">ma</tt><tt class="py-op">.</tt><tt class="py-name">masked_where</tt><tt class="py-op">(</tt><tt class="py-name">tomask</tt><tt class="py-op">,</tt> <tt class="py-name">resid</tt><tt class="py-op">)</tt> </tt>
<a name="L457"></a><tt class="py-lineno">457</tt>  <tt class="py-line">    <tt class="py-comment"># It makes more sense to me to have a minus sign here... So when the</tt> </tt>
<a name="L458"></a><tt class="py-lineno">458</tt>  <tt class="py-line">    <tt class="py-comment"># model is high, the residual is positive. This is opposite of the</tt> </tt>
<a name="L459"></a><tt class="py-lineno">459</tt>  <tt class="py-line">    <tt class="py-comment"># Pierce and Schafner convention.</tt> </tt>
<a name="L460"></a><tt class="py-lineno">460</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt class="py-name">resid</tt> </tt>
</div><a name="L461"></a><tt class="py-lineno">461</tt>  <tt class="py-line"> </tt>
<a name="optimally_scaled_sfs"></a><div id="optimally_scaled_sfs-def"><a name="L462"></a><tt class="py-lineno">462</tt> <a class="py-toggle" href="#" id="optimally_scaled_sfs-toggle" onclick="return toggle('optimally_scaled_sfs');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimally_scaled_sfs">optimally_scaled_sfs</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimally_scaled_sfs-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimally_scaled_sfs-expanded"><a name="L463"></a><tt class="py-lineno">463</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L464"></a><tt class="py-lineno">464</tt>  <tt class="py-line"><tt class="py-docstring">    Optimially scale model sfs to data sfs.</tt> </tt>
<a name="L465"></a><tt class="py-lineno">465</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L466"></a><tt class="py-lineno">466</tt>  <tt class="py-line"><tt class="py-docstring">    Returns a new scaled model sfs.</tt> </tt>
<a name="L467"></a><tt class="py-lineno">467</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L468"></a><tt class="py-lineno">468</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-52" class="py-name"><a title="dadi.Inference.optimal_sfs_scaling" class="py-name" href="#" onclick="return doclink('link-52', 'optimal_sfs_scaling', 'link-18');">optimal_sfs_scaling</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt><tt class="py-name">data</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">model</tt> </tt>
</div><a name="L469"></a><tt class="py-lineno">469</tt>  <tt class="py-line"> </tt>
<a name="optimal_sfs_scaling"></a><div id="optimal_sfs_scaling-def"><a name="L470"></a><tt class="py-lineno">470</tt> <a class="py-toggle" href="#" id="optimal_sfs_scaling-toggle" onclick="return toggle('optimal_sfs_scaling');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimal_sfs_scaling">optimal_sfs_scaling</a><tt class="py-op">(</tt><tt class="py-param">model</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimal_sfs_scaling-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimal_sfs_scaling-expanded"><a name="L471"></a><tt class="py-lineno">471</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L472"></a><tt class="py-lineno">472</tt>  <tt class="py-line"><tt class="py-docstring">    Optimal multiplicative scaling factor between model and data.</tt> </tt>
<a name="L473"></a><tt class="py-lineno">473</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L474"></a><tt class="py-lineno">474</tt>  <tt class="py-line"><tt class="py-docstring">    This scaling is based on only those entries that are masked in neither</tt> </tt>
<a name="L475"></a><tt class="py-lineno">475</tt>  <tt class="py-line"><tt class="py-docstring">    model nor data.</tt> </tt>
<a name="L476"></a><tt class="py-lineno">476</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L477"></a><tt class="py-lineno">477</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt> <tt class="py-keyword">and</tt> <tt class="py-keyword">not</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt class="py-name">folded</tt><tt class="py-op">:</tt> </tt>
<a name="L478"></a><tt class="py-lineno">478</tt>  <tt class="py-line">        <tt class="py-name">model</tt> <tt class="py-op">=</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt id="link-53" class="py-name"><a title="dadi.Spectrum_mod.Spectrum.fold" class="py-name" href="#" onclick="return doclink('link-53', 'fold', 'link-37');">fold</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L479"></a><tt class="py-lineno">479</tt>  <tt class="py-line"> </tt>
<a name="L480"></a><tt class="py-lineno">480</tt>  <tt class="py-line">    <tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt> <tt class="py-op">=</tt> <tt id="link-54" class="py-name"><a title="dadi.Numerics" class="py-name" href="#" onclick="return doclink('link-54', 'Numerics', 'link-3');">Numerics</a></tt><tt class="py-op">.</tt><tt id="link-55" class="py-name" targets="Function dadi.Numerics.intersect_masks()=dadi.Numerics-module.html#intersect_masks"><a title="dadi.Numerics.intersect_masks" class="py-name" href="#" onclick="return doclink('link-55', 'intersect_masks', 'link-55');">intersect_masks</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt class="py-name">data</tt><tt class="py-op">)</tt> </tt>
<a name="L481"></a><tt class="py-lineno">481</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">data</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-name">model</tt><tt class="py-op">.</tt><tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L482"></a><tt class="py-lineno">482</tt>  <tt class="py-line"> </tt>
<a name="optimize_log_fmin"></a><div id="optimize_log_fmin-def"><a name="L483"></a><tt class="py-lineno">483</tt> <a class="py-toggle" href="#" id="optimize_log_fmin-toggle" onclick="return toggle('optimize_log_fmin');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimize_log_fmin">optimize_log_fmin</a><tt class="py-op">(</tt><tt class="py-param">p0</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">model_func</tt><tt class="py-op">,</tt> <tt class="py-param">pts</tt><tt class="py-op">,</tt>  </tt>
<a name="L484"></a><tt class="py-lineno">484</tt>  <tt class="py-line">                      <tt class="py-param">lower_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">upper_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> </tt>
<a name="L485"></a><tt class="py-lineno">485</tt>  <tt class="py-line">                      <tt class="py-param">verbose</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">flush_delay</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt>  </tt>
<a name="L486"></a><tt class="py-lineno">486</tt>  <tt class="py-line">                      <tt class="py-param">multinom</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-param">maxiter</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt>  </tt>
<a name="L487"></a><tt class="py-lineno">487</tt>  <tt class="py-line">                      <tt class="py-param">full_output</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-param">func_args</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt>  </tt>
<a name="L488"></a><tt class="py-lineno">488</tt>  <tt class="py-line">                      <tt class="py-param">func_kwargs</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">,</tt> </tt>
<a name="L489"></a><tt class="py-lineno">489</tt>  <tt class="py-line">                      <tt class="py-param">fixed_params</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">output_file</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimize_log_fmin-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimize_log_fmin-expanded"><a name="L490"></a><tt class="py-lineno">490</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L491"></a><tt class="py-lineno">491</tt>  <tt class="py-line"><tt class="py-docstring">    Optimize log(params) to fit model to data using Nelder-Mead. </tt> </tt>
<a name="L492"></a><tt class="py-lineno">492</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L493"></a><tt class="py-lineno">493</tt>  <tt class="py-line"><tt class="py-docstring">    This optimization method may work better than BFGS when far from a</tt> </tt>
<a name="L494"></a><tt class="py-lineno">494</tt>  <tt class="py-line"><tt class="py-docstring">    minimum. It is much slower, but more robust, because it doesn't use</tt> </tt>
<a name="L495"></a><tt class="py-lineno">495</tt>  <tt class="py-line"><tt class="py-docstring">    gradient information.</tt> </tt>
<a name="L496"></a><tt class="py-lineno">496</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L497"></a><tt class="py-lineno">497</tt>  <tt class="py-line"><tt class="py-docstring">    Because this works in log(params), it cannot explore values of params &lt; 0.</tt> </tt>
<a name="L498"></a><tt class="py-lineno">498</tt>  <tt class="py-line"><tt class="py-docstring">    It should also perform better when parameters range over large scales.</tt> </tt>
<a name="L499"></a><tt class="py-lineno">499</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L500"></a><tt class="py-lineno">500</tt>  <tt class="py-line"><tt class="py-docstring">    p0: Initial parameters.</tt> </tt>
<a name="L501"></a><tt class="py-lineno">501</tt>  <tt class="py-line"><tt class="py-docstring">    data: Spectrum with data.</tt> </tt>
<a name="L502"></a><tt class="py-lineno">502</tt>  <tt class="py-line"><tt class="py-docstring">    model_function: Function to evaluate model spectrum. Should take arguments</tt> </tt>
<a name="L503"></a><tt class="py-lineno">503</tt>  <tt class="py-line"><tt class="py-docstring">                    (params, (n1,n2...), pts)</tt> </tt>
<a name="L504"></a><tt class="py-lineno">504</tt>  <tt class="py-line"><tt class="py-docstring">    lower_bound: Lower bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L505"></a><tt class="py-lineno">505</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0. A parameter can be declared unbound by assigning</tt> </tt>
<a name="L506"></a><tt class="py-lineno">506</tt>  <tt class="py-line"><tt class="py-docstring">                 a bound of None.</tt> </tt>
<a name="L507"></a><tt class="py-lineno">507</tt>  <tt class="py-line"><tt class="py-docstring">    upper_bound: Upper bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L508"></a><tt class="py-lineno">508</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0. A parameter can be declared unbound by assigning</tt> </tt>
<a name="L509"></a><tt class="py-lineno">509</tt>  <tt class="py-line"><tt class="py-docstring">                 a bound of None.</tt> </tt>
<a name="L510"></a><tt class="py-lineno">510</tt>  <tt class="py-line"><tt class="py-docstring">    verbose: If True, print optimization status every &lt;verbose&gt; steps.</tt> </tt>
<a name="L511"></a><tt class="py-lineno">511</tt>  <tt class="py-line"><tt class="py-docstring">    output_file: Stream verbose output into this filename. If None, stream to</tt> </tt>
<a name="L512"></a><tt class="py-lineno">512</tt>  <tt class="py-line"><tt class="py-docstring">                 standard out.</tt> </tt>
<a name="L513"></a><tt class="py-lineno">513</tt>  <tt class="py-line"><tt class="py-docstring">    flush_delay: Standard output will be flushed once every &lt;flush_delay&gt;</tt> </tt>
<a name="L514"></a><tt class="py-lineno">514</tt>  <tt class="py-line"><tt class="py-docstring">                 minutes. This is useful to avoid overloading I/O on clusters.</tt> </tt>
<a name="L515"></a><tt class="py-lineno">515</tt>  <tt class="py-line"><tt class="py-docstring">    multinom: If True, do a multinomial fit where model is optimially scaled to</tt> </tt>
<a name="L516"></a><tt class="py-lineno">516</tt>  <tt class="py-line"><tt class="py-docstring">              data at each step. If False, assume theta is a parameter and do</tt> </tt>
<a name="L517"></a><tt class="py-lineno">517</tt>  <tt class="py-line"><tt class="py-docstring">              no scaling.</tt> </tt>
<a name="L518"></a><tt class="py-lineno">518</tt>  <tt class="py-line"><tt class="py-docstring">    maxiter: Maximum iterations to run for.</tt> </tt>
<a name="L519"></a><tt class="py-lineno">519</tt>  <tt class="py-line"><tt class="py-docstring">    full_output: If True, return full outputs as in described in </tt> </tt>
<a name="L520"></a><tt class="py-lineno">520</tt>  <tt class="py-line"><tt class="py-docstring">                 help(scipy.optimize.fmin_bfgs)</tt> </tt>
<a name="L521"></a><tt class="py-lineno">521</tt>  <tt class="py-line"><tt class="py-docstring">    func_args: Additional arguments to model_func. It is assumed that </tt> </tt>
<a name="L522"></a><tt class="py-lineno">522</tt>  <tt class="py-line"><tt class="py-docstring">               model_func's first argument is an array of parameters to</tt> </tt>
<a name="L523"></a><tt class="py-lineno">523</tt>  <tt class="py-line"><tt class="py-docstring">               optimize, that its second argument is an array of sample sizes</tt> </tt>
<a name="L524"></a><tt class="py-lineno">524</tt>  <tt class="py-line"><tt class="py-docstring">               for the sfs, and that its last argument is the list of grid</tt> </tt>
<a name="L525"></a><tt class="py-lineno">525</tt>  <tt class="py-line"><tt class="py-docstring">               points to use in evaluation.</tt> </tt>
<a name="L526"></a><tt class="py-lineno">526</tt>  <tt class="py-line"><tt class="py-docstring">    func_kwargs: Additional keyword arguments to model_func.</tt> </tt>
<a name="L527"></a><tt class="py-lineno">527</tt>  <tt class="py-line"><tt class="py-docstring">    fixed_params: If not None, should be a list used to fix model parameters at</tt> </tt>
<a name="L528"></a><tt class="py-lineno">528</tt>  <tt class="py-line"><tt class="py-docstring">                  particular values. For example, if the model parameters</tt> </tt>
<a name="L529"></a><tt class="py-lineno">529</tt>  <tt class="py-line"><tt class="py-docstring">                  are (nu1,nu2,T,m), then fixed_params = [0.5,None,None,2]</tt> </tt>
<a name="L530"></a><tt class="py-lineno">530</tt>  <tt class="py-line"><tt class="py-docstring">                  will hold nu1=0.5 and m=2. The optimizer will only change </tt> </tt>
<a name="L531"></a><tt class="py-lineno">531</tt>  <tt class="py-line"><tt class="py-docstring">                  T and m. Note that the bounds lists must include all</tt> </tt>
<a name="L532"></a><tt class="py-lineno">532</tt>  <tt class="py-line"><tt class="py-docstring">                  parameters. Optimization will fail if the fixed values</tt> </tt>
<a name="L533"></a><tt class="py-lineno">533</tt>  <tt class="py-line"><tt class="py-docstring">                  lie outside their bounds. A full-length p0 should be passed</tt> </tt>
<a name="L534"></a><tt class="py-lineno">534</tt>  <tt class="py-line"><tt class="py-docstring">                  in; values corresponding to fixed parameters are ignored.</tt> </tt>
<a name="L535"></a><tt class="py-lineno">535</tt>  <tt class="py-line"><tt class="py-docstring">    (See help(dadi.Inference.optimize_log for examples of func_args and </tt> </tt>
<a name="L536"></a><tt class="py-lineno">536</tt>  <tt class="py-line"><tt class="py-docstring">     fixed_params usage.)</tt> </tt>
<a name="L537"></a><tt class="py-lineno">537</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L538"></a><tt class="py-lineno">538</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L539"></a><tt class="py-lineno">539</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">file</tt><tt class="py-op">(</tt><tt class="py-name">output_file</tt><tt class="py-op">,</tt> <tt class="py-string">'w'</tt><tt class="py-op">)</tt> </tt>
<a name="L540"></a><tt class="py-lineno">540</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L541"></a><tt class="py-lineno">541</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">sys</tt><tt class="py-op">.</tt><tt class="py-name">stdout</tt> </tt>
<a name="L542"></a><tt class="py-lineno">542</tt>  <tt class="py-line"> </tt>
<a name="L543"></a><tt class="py-lineno">543</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">,</tt> <tt class="py-name">model_func</tt><tt class="py-op">,</tt> <tt class="py-name">pts</tt><tt class="py-op">,</tt> <tt class="py-name">lower_bound</tt><tt class="py-op">,</tt> <tt class="py-name">upper_bound</tt><tt class="py-op">,</tt> <tt class="py-name">verbose</tt><tt class="py-op">,</tt> </tt>
<a name="L544"></a><tt class="py-lineno">544</tt>  <tt class="py-line">            <tt class="py-name">multinom</tt><tt class="py-op">,</tt> <tt class="py-name">flush_delay</tt><tt class="py-op">,</tt> <tt class="py-name">func_args</tt><tt class="py-op">,</tt> <tt class="py-name">func_kwargs</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">,</tt> <tt class="py-number">1.0</tt><tt class="py-op">,</tt> </tt>
<a name="L545"></a><tt class="py-lineno">545</tt>  <tt class="py-line">            <tt class="py-name">output_stream</tt><tt class="py-op">)</tt> </tt>
<a name="L546"></a><tt class="py-lineno">546</tt>  <tt class="py-line"> </tt>
<a name="L547"></a><tt class="py-lineno">547</tt>  <tt class="py-line">    <tt class="py-name">p0</tt> <tt class="py-op">=</tt> <tt id="link-56" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-56', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L548"></a><tt class="py-lineno">548</tt>  <tt class="py-line">    <tt class="py-name">outputs</tt> <tt class="py-op">=</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt id="link-57" class="py-name"><a title="dadi.Inference.optimize" class="py-name" href="#" onclick="return doclink('link-57', 'optimize', 'link-4');">optimize</a></tt><tt class="py-op">.</tt><tt class="py-name">fmin</tt><tt class="py-op">(</tt><tt id="link-58" class="py-name"><a title="dadi.Inference._object_func_log" class="py-name" href="#" onclick="return doclink('link-58', '_object_func_log', 'link-27');">_object_func_log</a></tt><tt class="py-op">,</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">log</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">args</tt><tt class="py-op">,</tt> </tt>
<a name="L549"></a><tt class="py-lineno">549</tt>  <tt class="py-line">                                  <tt class="py-name">disp</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-name">maxiter</tt><tt class="py-op">=</tt><tt class="py-name">maxiter</tt><tt class="py-op">,</tt> <tt class="py-name">full_output</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">)</tt> </tt>
<a name="L550"></a><tt class="py-lineno">550</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">iter</tt><tt class="py-op">,</tt> <tt class="py-name">funcalls</tt><tt class="py-op">,</tt> <tt class="py-name">warnflag</tt> <tt class="py-op">=</tt> <tt class="py-name">outputs</tt> </tt>
<a name="L551"></a><tt class="py-lineno">551</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt> <tt class="py-op">=</tt> <tt id="link-59" class="py-name"><a title="dadi.Inference._project_params_up" class="py-name" href="#" onclick="return doclink('link-59', '_project_params_up', 'link-10');">_project_params_up</a></tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">exp</tt><tt class="py-op">(</tt><tt class="py-name">xopt</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L552"></a><tt class="py-lineno">552</tt>  <tt class="py-line"> </tt>
<a name="L553"></a><tt class="py-lineno">553</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L554"></a><tt class="py-lineno">554</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt><tt class="py-op">.</tt><tt class="py-name">close</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L555"></a><tt class="py-lineno">555</tt>  <tt class="py-line"> </tt>
<a name="L556"></a><tt class="py-lineno">556</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L557"></a><tt class="py-lineno">557</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt> </tt>
<a name="L558"></a><tt class="py-lineno">558</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L559"></a><tt class="py-lineno">559</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">iter</tt><tt class="py-op">,</tt> <tt class="py-name">funcalls</tt><tt class="py-op">,</tt> <tt class="py-name">warnflag</tt>  </tt>
</div><a name="L560"></a><tt class="py-lineno">560</tt>  <tt class="py-line"> </tt>
<a name="optimize"></a><div id="optimize-def"><a name="L561"></a><tt class="py-lineno">561</tt> <a class="py-toggle" href="#" id="optimize-toggle" onclick="return toggle('optimize');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimize">optimize</a><tt class="py-op">(</tt><tt class="py-param">p0</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">model_func</tt><tt class="py-op">,</tt> <tt class="py-param">pts</tt><tt class="py-op">,</tt> <tt class="py-param">lower_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">upper_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> </tt>
<a name="L562"></a><tt class="py-lineno">562</tt>  <tt class="py-line">             <tt class="py-param">verbose</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">flush_delay</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">epsilon</tt><tt class="py-op">=</tt><tt class="py-number">1e-3</tt><tt class="py-op">,</tt>  </tt>
<a name="L563"></a><tt class="py-lineno">563</tt>  <tt class="py-line">             <tt class="py-param">gtol</tt><tt class="py-op">=</tt><tt class="py-number">1e-5</tt><tt class="py-op">,</tt> <tt class="py-param">multinom</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-param">maxiter</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">full_output</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L564"></a><tt class="py-lineno">564</tt>  <tt class="py-line">             <tt class="py-param">func_args</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-param">func_kwargs</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">ll_scale</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> </tt>
<a name="L565"></a><tt class="py-lineno">565</tt>  <tt class="py-line">             <tt class="py-param">output_file</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimize-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimize-expanded"><a name="L566"></a><tt class="py-lineno">566</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L567"></a><tt class="py-lineno">567</tt>  <tt class="py-line"><tt class="py-docstring">    Optimize params to fit model to data using the BFGS method.</tt> </tt>
<a name="L568"></a><tt class="py-lineno">568</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L569"></a><tt class="py-lineno">569</tt>  <tt class="py-line"><tt class="py-docstring">    This optimization method works well when we start reasonably close to the</tt> </tt>
<a name="L570"></a><tt class="py-lineno">570</tt>  <tt class="py-line"><tt class="py-docstring">    optimum. It is best at burrowing down a single minimum.</tt> </tt>
<a name="L571"></a><tt class="py-lineno">571</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L572"></a><tt class="py-lineno">572</tt>  <tt class="py-line"><tt class="py-docstring">    p0: Initial parameters.</tt> </tt>
<a name="L573"></a><tt class="py-lineno">573</tt>  <tt class="py-line"><tt class="py-docstring">    data: Spectrum with data.</tt> </tt>
<a name="L574"></a><tt class="py-lineno">574</tt>  <tt class="py-line"><tt class="py-docstring">    model_function: Function to evaluate model spectrum. Should take arguments</tt> </tt>
<a name="L575"></a><tt class="py-lineno">575</tt>  <tt class="py-line"><tt class="py-docstring">                    (params, (n1,n2...), pts)</tt> </tt>
<a name="L576"></a><tt class="py-lineno">576</tt>  <tt class="py-line"><tt class="py-docstring">    lower_bound: Lower bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L577"></a><tt class="py-lineno">577</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0.</tt> </tt>
<a name="L578"></a><tt class="py-lineno">578</tt>  <tt class="py-line"><tt class="py-docstring">    upper_bound: Upper bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L579"></a><tt class="py-lineno">579</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0.</tt> </tt>
<a name="L580"></a><tt class="py-lineno">580</tt>  <tt class="py-line"><tt class="py-docstring">    verbose: If &gt; 0, print optimization status every &lt;verbose&gt; steps.</tt> </tt>
<a name="L581"></a><tt class="py-lineno">581</tt>  <tt class="py-line"><tt class="py-docstring">    output_file: Stream verbose output into this filename. If None, stream to</tt> </tt>
<a name="L582"></a><tt class="py-lineno">582</tt>  <tt class="py-line"><tt class="py-docstring">                 standard out.</tt> </tt>
<a name="L583"></a><tt class="py-lineno">583</tt>  <tt class="py-line"><tt class="py-docstring">    flush_delay: Standard output will be flushed once every &lt;flush_delay&gt;</tt> </tt>
<a name="L584"></a><tt class="py-lineno">584</tt>  <tt class="py-line"><tt class="py-docstring">                 minutes. This is useful to avoid overloading I/O on clusters.</tt> </tt>
<a name="L585"></a><tt class="py-lineno">585</tt>  <tt class="py-line"><tt class="py-docstring">    epsilon: Step-size to use for finite-difference derivatives.</tt> </tt>
<a name="L586"></a><tt class="py-lineno">586</tt>  <tt class="py-line"><tt class="py-docstring">    gtol: Convergence criterion for optimization. For more info, </tt> </tt>
<a name="L587"></a><tt class="py-lineno">587</tt>  <tt class="py-line"><tt class="py-docstring">          see help(scipy.optimize.fmin_bfgs)</tt> </tt>
<a name="L588"></a><tt class="py-lineno">588</tt>  <tt class="py-line"><tt class="py-docstring">    multinom: If True, do a multinomial fit where model is optimially scaled to</tt> </tt>
<a name="L589"></a><tt class="py-lineno">589</tt>  <tt class="py-line"><tt class="py-docstring">              data at each step. If False, assume theta is a parameter and do</tt> </tt>
<a name="L590"></a><tt class="py-lineno">590</tt>  <tt class="py-line"><tt class="py-docstring">              no scaling.</tt> </tt>
<a name="L591"></a><tt class="py-lineno">591</tt>  <tt class="py-line"><tt class="py-docstring">    maxiter: Maximum iterations to run for.</tt> </tt>
<a name="L592"></a><tt class="py-lineno">592</tt>  <tt class="py-line"><tt class="py-docstring">    full_output: If True, return full outputs as in described in </tt> </tt>
<a name="L593"></a><tt class="py-lineno">593</tt>  <tt class="py-line"><tt class="py-docstring">                 help(scipy.optimize.fmin_bfgs)</tt> </tt>
<a name="L594"></a><tt class="py-lineno">594</tt>  <tt class="py-line"><tt class="py-docstring">    func_args: Additional arguments to model_func. It is assumed that </tt> </tt>
<a name="L595"></a><tt class="py-lineno">595</tt>  <tt class="py-line"><tt class="py-docstring">               model_func's first argument is an array of parameters to</tt> </tt>
<a name="L596"></a><tt class="py-lineno">596</tt>  <tt class="py-line"><tt class="py-docstring">               optimize, that its second argument is an array of sample sizes</tt> </tt>
<a name="L597"></a><tt class="py-lineno">597</tt>  <tt class="py-line"><tt class="py-docstring">               for the sfs, and that its last argument is the list of grid</tt> </tt>
<a name="L598"></a><tt class="py-lineno">598</tt>  <tt class="py-line"><tt class="py-docstring">               points to use in evaluation.</tt> </tt>
<a name="L599"></a><tt class="py-lineno">599</tt>  <tt class="py-line"><tt class="py-docstring">    func_kwargs: Additional keyword arguments to model_func.</tt> </tt>
<a name="L600"></a><tt class="py-lineno">600</tt>  <tt class="py-line"><tt class="py-docstring">    fixed_params: If not None, should be a list used to fix model parameters at</tt> </tt>
<a name="L601"></a><tt class="py-lineno">601</tt>  <tt class="py-line"><tt class="py-docstring">                  particular values. For example, if the model parameters</tt> </tt>
<a name="L602"></a><tt class="py-lineno">602</tt>  <tt class="py-line"><tt class="py-docstring">                  are (nu1,nu2,T,m), then fixed_params = [0.5,None,None,2]</tt> </tt>
<a name="L603"></a><tt class="py-lineno">603</tt>  <tt class="py-line"><tt class="py-docstring">                  will hold nu1=0.5 and m=2. The optimizer will only change </tt> </tt>
<a name="L604"></a><tt class="py-lineno">604</tt>  <tt class="py-line"><tt class="py-docstring">                  T and m. Note that the bounds lists must include all</tt> </tt>
<a name="L605"></a><tt class="py-lineno">605</tt>  <tt class="py-line"><tt class="py-docstring">                  parameters. Optimization will fail if the fixed values</tt> </tt>
<a name="L606"></a><tt class="py-lineno">606</tt>  <tt class="py-line"><tt class="py-docstring">                  lie outside their bounds. A full-length p0 should be passed</tt> </tt>
<a name="L607"></a><tt class="py-lineno">607</tt>  <tt class="py-line"><tt class="py-docstring">                  in; values corresponding to fixed parameters are ignored.</tt> </tt>
<a name="L608"></a><tt class="py-lineno">608</tt>  <tt class="py-line"><tt class="py-docstring">    (See help(dadi.Inference.optimize_log for examples of func_args and </tt> </tt>
<a name="L609"></a><tt class="py-lineno">609</tt>  <tt class="py-line"><tt class="py-docstring">     fixed_params usage.)</tt> </tt>
<a name="L610"></a><tt class="py-lineno">610</tt>  <tt class="py-line"><tt class="py-docstring">    ll_scale: The bfgs algorithm may fail if your initial log-likelihood is</tt> </tt>
<a name="L611"></a><tt class="py-lineno">611</tt>  <tt class="py-line"><tt class="py-docstring">              too large. (This appears to be a flaw in the scipy</tt> </tt>
<a name="L612"></a><tt class="py-lineno">612</tt>  <tt class="py-line"><tt class="py-docstring">              implementation.) To overcome this, pass ll_scale &gt; 1, which will</tt> </tt>
<a name="L613"></a><tt class="py-lineno">613</tt>  <tt class="py-line"><tt class="py-docstring">              simply reduce the magnitude of the log-likelihood. Once in a</tt> </tt>
<a name="L614"></a><tt class="py-lineno">614</tt>  <tt class="py-line"><tt class="py-docstring">              region of reasonable likelihood, you'll probably want to</tt> </tt>
<a name="L615"></a><tt class="py-lineno">615</tt>  <tt class="py-line"><tt class="py-docstring">              re-optimize with ll_scale=1.</tt> </tt>
<a name="L616"></a><tt class="py-lineno">616</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L617"></a><tt class="py-lineno">617</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L618"></a><tt class="py-lineno">618</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">file</tt><tt class="py-op">(</tt><tt class="py-name">output_file</tt><tt class="py-op">,</tt> <tt class="py-string">'w'</tt><tt class="py-op">)</tt> </tt>
<a name="L619"></a><tt class="py-lineno">619</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L620"></a><tt class="py-lineno">620</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">sys</tt><tt class="py-op">.</tt><tt class="py-name">stdout</tt> </tt>
<a name="L621"></a><tt class="py-lineno">621</tt>  <tt class="py-line"> </tt>
<a name="L622"></a><tt class="py-lineno">622</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">,</tt> <tt class="py-name">model_func</tt><tt class="py-op">,</tt> <tt class="py-name">pts</tt><tt class="py-op">,</tt> <tt class="py-name">lower_bound</tt><tt class="py-op">,</tt> <tt class="py-name">upper_bound</tt><tt class="py-op">,</tt> <tt class="py-name">verbose</tt><tt class="py-op">,</tt> </tt>
<a name="L623"></a><tt class="py-lineno">623</tt>  <tt class="py-line">            <tt class="py-name">multinom</tt><tt class="py-op">,</tt> <tt class="py-name">flush_delay</tt><tt class="py-op">,</tt> <tt class="py-name">func_args</tt><tt class="py-op">,</tt> <tt class="py-name">func_kwargs</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">,</tt>  </tt>
<a name="L624"></a><tt class="py-lineno">624</tt>  <tt class="py-line">            <tt class="py-name">ll_scale</tt><tt class="py-op">,</tt> <tt class="py-name">output_stream</tt><tt class="py-op">)</tt> </tt>
<a name="L625"></a><tt class="py-lineno">625</tt>  <tt class="py-line"> </tt>
<a name="L626"></a><tt class="py-lineno">626</tt>  <tt class="py-line">    <tt class="py-name">p0</tt> <tt class="py-op">=</tt> <tt id="link-60" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-60', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L627"></a><tt class="py-lineno">627</tt>  <tt class="py-line">    <tt class="py-name">outputs</tt> <tt class="py-op">=</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt id="link-61" class="py-name"><a title="dadi.Inference.optimize" class="py-name" href="#" onclick="return doclink('link-61', 'optimize', 'link-4');">optimize</a></tt><tt class="py-op">.</tt><tt class="py-name">fmin_bfgs</tt><tt class="py-op">(</tt><tt id="link-62" class="py-name"><a title="dadi.Inference._object_func" class="py-name" href="#" onclick="return doclink('link-62', '_object_func', 'link-24');">_object_func</a></tt><tt class="py-op">,</tt> <tt class="py-name">p0</tt><tt class="py-op">,</tt>  </tt>
<a name="L628"></a><tt class="py-lineno">628</tt>  <tt class="py-line">                                       <tt class="py-name">epsilon</tt><tt class="py-op">=</tt><tt class="py-name">epsilon</tt><tt class="py-op">,</tt> </tt>
<a name="L629"></a><tt class="py-lineno">629</tt>  <tt class="py-line">                                       <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">args</tt><tt class="py-op">,</tt> <tt class="py-name">gtol</tt><tt class="py-op">=</tt><tt class="py-name">gtol</tt><tt class="py-op">,</tt>  </tt>
<a name="L630"></a><tt class="py-lineno">630</tt>  <tt class="py-line">                                       <tt class="py-name">full_output</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> </tt>
<a name="L631"></a><tt class="py-lineno">631</tt>  <tt class="py-line">                                       <tt class="py-name">disp</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L632"></a><tt class="py-lineno">632</tt>  <tt class="py-line">                                       <tt class="py-name">maxiter</tt><tt class="py-op">=</tt><tt class="py-name">maxiter</tt><tt class="py-op">)</tt> </tt>
<a name="L633"></a><tt class="py-lineno">633</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">gopt</tt><tt class="py-op">,</tt> <tt class="py-name">Bopt</tt><tt class="py-op">,</tt> <tt class="py-name">func_calls</tt><tt class="py-op">,</tt> <tt class="py-name">grad_calls</tt><tt class="py-op">,</tt> <tt class="py-name">warnflag</tt> <tt class="py-op">=</tt> <tt class="py-name">outputs</tt> </tt>
<a name="L634"></a><tt class="py-lineno">634</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt> <tt class="py-op">=</tt> <tt id="link-63" class="py-name"><a title="dadi.Inference._project_params_up" class="py-name" href="#" onclick="return doclink('link-63', '_project_params_up', 'link-10');">_project_params_up</a></tt><tt class="py-op">(</tt><tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L635"></a><tt class="py-lineno">635</tt>  <tt class="py-line"> </tt>
<a name="L636"></a><tt class="py-lineno">636</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L637"></a><tt class="py-lineno">637</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt><tt class="py-op">.</tt><tt class="py-name">close</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L638"></a><tt class="py-lineno">638</tt>  <tt class="py-line"> </tt>
<a name="L639"></a><tt class="py-lineno">639</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L640"></a><tt class="py-lineno">640</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt> </tt>
<a name="L641"></a><tt class="py-lineno">641</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L642"></a><tt class="py-lineno">642</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">gopt</tt><tt class="py-op">,</tt> <tt class="py-name">Bopt</tt><tt class="py-op">,</tt> <tt class="py-name">func_calls</tt><tt class="py-op">,</tt> <tt class="py-name">grad_calls</tt><tt class="py-op">,</tt> <tt class="py-name">warnflag</tt> </tt>
</div><a name="L643"></a><tt class="py-lineno">643</tt>  <tt class="py-line"> </tt>
<a name="L644"></a><tt class="py-lineno">644</tt>  <tt class="py-line"> </tt>
<a name="optimize_lbfgsb"></a><div id="optimize_lbfgsb-def"><a name="L645"></a><tt class="py-lineno">645</tt> <a class="py-toggle" href="#" id="optimize_lbfgsb-toggle" onclick="return toggle('optimize_lbfgsb');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimize_lbfgsb">optimize_lbfgsb</a><tt class="py-op">(</tt><tt class="py-param">p0</tt><tt class="py-op">,</tt> <tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">model_func</tt><tt class="py-op">,</tt> <tt class="py-param">pts</tt><tt class="py-op">,</tt>  </tt>
<a name="L646"></a><tt class="py-lineno">646</tt>  <tt class="py-line">                    <tt class="py-param">lower_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-param">upper_bound</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> </tt>
<a name="L647"></a><tt class="py-lineno">647</tt>  <tt class="py-line">                    <tt class="py-param">verbose</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">flush_delay</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">epsilon</tt><tt class="py-op">=</tt><tt class="py-number">1e-3</tt><tt class="py-op">,</tt>  </tt>
<a name="L648"></a><tt class="py-lineno">648</tt>  <tt class="py-line">                    <tt class="py-param">pgtol</tt><tt class="py-op">=</tt><tt class="py-number">1e-5</tt><tt class="py-op">,</tt> <tt class="py-param">multinom</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-param">maxiter</tt><tt class="py-op">=</tt><tt class="py-number">1e5</tt><tt class="py-op">,</tt> <tt class="py-param">full_output</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L649"></a><tt class="py-lineno">649</tt>  <tt class="py-line">                    <tt class="py-param">func_args</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-param">func_kwargs</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt>  </tt>
<a name="L650"></a><tt class="py-lineno">650</tt>  <tt class="py-line">                    <tt class="py-param">ll_scale</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">output_file</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimize_lbfgsb-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimize_lbfgsb-expanded"><a name="L651"></a><tt class="py-lineno">651</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L652"></a><tt class="py-lineno">652</tt>  <tt class="py-line"><tt class="py-docstring">    Optimize log(params) to fit model to data using the L-BFGS-B method.</tt> </tt>
<a name="L653"></a><tt class="py-lineno">653</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L654"></a><tt class="py-lineno">654</tt>  <tt class="py-line"><tt class="py-docstring">    This optimization method works well when we start reasonably close to the</tt> </tt>
<a name="L655"></a><tt class="py-lineno">655</tt>  <tt class="py-line"><tt class="py-docstring">    optimum. It is best at burrowing down a single minimum. This method is</tt> </tt>
<a name="L656"></a><tt class="py-lineno">656</tt>  <tt class="py-line"><tt class="py-docstring">    better than optimize_log if the optimum lies at one or more of the</tt> </tt>
<a name="L657"></a><tt class="py-lineno">657</tt>  <tt class="py-line"><tt class="py-docstring">    parameter bounds. However, if your optimum is not on the bounds, this</tt> </tt>
<a name="L658"></a><tt class="py-lineno">658</tt>  <tt class="py-line"><tt class="py-docstring">    method may be much slower.</tt> </tt>
<a name="L659"></a><tt class="py-lineno">659</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L660"></a><tt class="py-lineno">660</tt>  <tt class="py-line"><tt class="py-docstring">    p0: Initial parameters.</tt> </tt>
<a name="L661"></a><tt class="py-lineno">661</tt>  <tt class="py-line"><tt class="py-docstring">    data: Spectrum with data.</tt> </tt>
<a name="L662"></a><tt class="py-lineno">662</tt>  <tt class="py-line"><tt class="py-docstring">    model_function: Function to evaluate model spectrum. Should take arguments</tt> </tt>
<a name="L663"></a><tt class="py-lineno">663</tt>  <tt class="py-line"><tt class="py-docstring">                    (params, (n1,n2...), pts)</tt> </tt>
<a name="L664"></a><tt class="py-lineno">664</tt>  <tt class="py-line"><tt class="py-docstring">    lower_bound: Lower bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L665"></a><tt class="py-lineno">665</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0. A parameter can be declared unbound by assigning</tt> </tt>
<a name="L666"></a><tt class="py-lineno">666</tt>  <tt class="py-line"><tt class="py-docstring">                 a bound of None.</tt> </tt>
<a name="L667"></a><tt class="py-lineno">667</tt>  <tt class="py-line"><tt class="py-docstring">    upper_bound: Upper bound on parameter values. If not None, must be of same</tt> </tt>
<a name="L668"></a><tt class="py-lineno">668</tt>  <tt class="py-line"><tt class="py-docstring">                 length as p0. A parameter can be declared unbound by assigning</tt> </tt>
<a name="L669"></a><tt class="py-lineno">669</tt>  <tt class="py-line"><tt class="py-docstring">                 a bound of None.</tt> </tt>
<a name="L670"></a><tt class="py-lineno">670</tt>  <tt class="py-line"><tt class="py-docstring">    verbose: If &gt; 0, print optimization status every &lt;verbose&gt; steps.</tt> </tt>
<a name="L671"></a><tt class="py-lineno">671</tt>  <tt class="py-line"><tt class="py-docstring">    output_file: Stream verbose output into this filename. If None, stream to</tt> </tt>
<a name="L672"></a><tt class="py-lineno">672</tt>  <tt class="py-line"><tt class="py-docstring">                 standard out.</tt> </tt>
<a name="L673"></a><tt class="py-lineno">673</tt>  <tt class="py-line"><tt class="py-docstring">    flush_delay: Standard output will be flushed once every &lt;flush_delay&gt;</tt> </tt>
<a name="L674"></a><tt class="py-lineno">674</tt>  <tt class="py-line"><tt class="py-docstring">                 minutes. This is useful to avoid overloading I/O on clusters.</tt> </tt>
<a name="L675"></a><tt class="py-lineno">675</tt>  <tt class="py-line"><tt class="py-docstring">    epsilon: Step-size to use for finite-difference derivatives.</tt> </tt>
<a name="L676"></a><tt class="py-lineno">676</tt>  <tt class="py-line"><tt class="py-docstring">    pgtol: Convergence criterion for optimization. For more info, </tt> </tt>
<a name="L677"></a><tt class="py-lineno">677</tt>  <tt class="py-line"><tt class="py-docstring">          see help(scipy.optimize.fmin_l_bfgs_b)</tt> </tt>
<a name="L678"></a><tt class="py-lineno">678</tt>  <tt class="py-line"><tt class="py-docstring">    multinom: If True, do a multinomial fit where model is optimially scaled to</tt> </tt>
<a name="L679"></a><tt class="py-lineno">679</tt>  <tt class="py-line"><tt class="py-docstring">              data at each step. If False, assume theta is a parameter and do</tt> </tt>
<a name="L680"></a><tt class="py-lineno">680</tt>  <tt class="py-line"><tt class="py-docstring">              no scaling.</tt> </tt>
<a name="L681"></a><tt class="py-lineno">681</tt>  <tt class="py-line"><tt class="py-docstring">    maxiter: Maximum algorithm iterations evaluations to run.</tt> </tt>
<a name="L682"></a><tt class="py-lineno">682</tt>  <tt class="py-line"><tt class="py-docstring">    full_output: If True, return full outputs as in described in </tt> </tt>
<a name="L683"></a><tt class="py-lineno">683</tt>  <tt class="py-line"><tt class="py-docstring">                 help(scipy.optimize.fmin_bfgs)</tt> </tt>
<a name="L684"></a><tt class="py-lineno">684</tt>  <tt class="py-line"><tt class="py-docstring">    func_args: Additional arguments to model_func. It is assumed that </tt> </tt>
<a name="L685"></a><tt class="py-lineno">685</tt>  <tt class="py-line"><tt class="py-docstring">               model_func's first argument is an array of parameters to</tt> </tt>
<a name="L686"></a><tt class="py-lineno">686</tt>  <tt class="py-line"><tt class="py-docstring">               optimize, that its second argument is an array of sample sizes</tt> </tt>
<a name="L687"></a><tt class="py-lineno">687</tt>  <tt class="py-line"><tt class="py-docstring">               for the sfs, and that its last argument is the list of grid</tt> </tt>
<a name="L688"></a><tt class="py-lineno">688</tt>  <tt class="py-line"><tt class="py-docstring">               points to use in evaluation.</tt> </tt>
<a name="L689"></a><tt class="py-lineno">689</tt>  <tt class="py-line"><tt class="py-docstring">    func_kwargs: Additional keyword arguments to model_func.</tt> </tt>
<a name="L690"></a><tt class="py-lineno">690</tt>  <tt class="py-line"><tt class="py-docstring">    fixed_params: If not None, should be a list used to fix model parameters at</tt> </tt>
<a name="L691"></a><tt class="py-lineno">691</tt>  <tt class="py-line"><tt class="py-docstring">                  particular values. For example, if the model parameters</tt> </tt>
<a name="L692"></a><tt class="py-lineno">692</tt>  <tt class="py-line"><tt class="py-docstring">                  are (nu1,nu2,T,m), then fixed_params = [0.5,None,None,2]</tt> </tt>
<a name="L693"></a><tt class="py-lineno">693</tt>  <tt class="py-line"><tt class="py-docstring">                  will hold nu1=0.5 and m=2. The optimizer will only change </tt> </tt>
<a name="L694"></a><tt class="py-lineno">694</tt>  <tt class="py-line"><tt class="py-docstring">                  T and m. Note that the bounds lists must include all</tt> </tt>
<a name="L695"></a><tt class="py-lineno">695</tt>  <tt class="py-line"><tt class="py-docstring">                  parameters. Optimization will fail if the fixed values</tt> </tt>
<a name="L696"></a><tt class="py-lineno">696</tt>  <tt class="py-line"><tt class="py-docstring">                  lie outside their bounds. A full-length p0 should be passed</tt> </tt>
<a name="L697"></a><tt class="py-lineno">697</tt>  <tt class="py-line"><tt class="py-docstring">                  in; values corresponding to fixed parameters are ignored.</tt> </tt>
<a name="L698"></a><tt class="py-lineno">698</tt>  <tt class="py-line"><tt class="py-docstring">    (See help(dadi.Inference.optimize_log for examples of func_args and </tt> </tt>
<a name="L699"></a><tt class="py-lineno">699</tt>  <tt class="py-line"><tt class="py-docstring">     fixed_params usage.)</tt> </tt>
<a name="L700"></a><tt class="py-lineno">700</tt>  <tt class="py-line"><tt class="py-docstring">    ll_scale: The bfgs algorithm may fail if your initial log-likelihood is</tt> </tt>
<a name="L701"></a><tt class="py-lineno">701</tt>  <tt class="py-line"><tt class="py-docstring">              too large. (This appears to be a flaw in the scipy</tt> </tt>
<a name="L702"></a><tt class="py-lineno">702</tt>  <tt class="py-line"><tt class="py-docstring">              implementation.) To overcome this, pass ll_scale &gt; 1, which will</tt> </tt>
<a name="L703"></a><tt class="py-lineno">703</tt>  <tt class="py-line"><tt class="py-docstring">              simply reduce the magnitude of the log-likelihood. Once in a</tt> </tt>
<a name="L704"></a><tt class="py-lineno">704</tt>  <tt class="py-line"><tt class="py-docstring">              region of reasonable likelihood, you'll probably want to</tt> </tt>
<a name="L705"></a><tt class="py-lineno">705</tt>  <tt class="py-line"><tt class="py-docstring">              re-optimize with ll_scale=1.</tt> </tt>
<a name="L706"></a><tt class="py-lineno">706</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L707"></a><tt class="py-lineno">707</tt>  <tt class="py-line"><tt class="py-docstring">    The L-BFGS-B method was developed by Ciyou Zhu, Richard Byrd, and Jorge</tt> </tt>
<a name="L708"></a><tt class="py-lineno">708</tt>  <tt class="py-line"><tt class="py-docstring">    Nocedal. The algorithm is described in:</tt> </tt>
<a name="L709"></a><tt class="py-lineno">709</tt>  <tt class="py-line"><tt class="py-docstring">      * R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound</tt> </tt>
<a name="L710"></a><tt class="py-lineno">710</tt>  <tt class="py-line"><tt class="py-docstring">        Constrained Optimization, (1995), SIAM Journal on Scientific and</tt> </tt>
<a name="L711"></a><tt class="py-lineno">711</tt>  <tt class="py-line"><tt class="py-docstring">        Statistical Computing , 16, 5, pp. 1190-1208.</tt> </tt>
<a name="L712"></a><tt class="py-lineno">712</tt>  <tt class="py-line"><tt class="py-docstring">      * C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B,</tt> </tt>
<a name="L713"></a><tt class="py-lineno">713</tt>  <tt class="py-line"><tt class="py-docstring">        FORTRAN routines for large scale bound constrained optimization (1997),</tt> </tt>
<a name="L714"></a><tt class="py-lineno">714</tt>  <tt class="py-line"><tt class="py-docstring">        ACM Transactions on Mathematical Software, Vol 23, Num. 4, pp. 550-560.</tt> </tt>
<a name="L715"></a><tt class="py-lineno">715</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L716"></a><tt class="py-lineno">716</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L717"></a><tt class="py-lineno">717</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">file</tt><tt class="py-op">(</tt><tt class="py-name">output_file</tt><tt class="py-op">,</tt> <tt class="py-string">'w'</tt><tt class="py-op">)</tt> </tt>
<a name="L718"></a><tt class="py-lineno">718</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L719"></a><tt class="py-lineno">719</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">sys</tt><tt class="py-op">.</tt><tt class="py-name">stdout</tt> </tt>
<a name="L720"></a><tt class="py-lineno">720</tt>  <tt class="py-line"> </tt>
<a name="L721"></a><tt class="py-lineno">721</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">,</tt> <tt class="py-name">model_func</tt><tt class="py-op">,</tt> <tt class="py-name">pts</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">verbose</tt><tt class="py-op">,</tt> </tt>
<a name="L722"></a><tt class="py-lineno">722</tt>  <tt class="py-line">            <tt class="py-name">multinom</tt><tt class="py-op">,</tt> <tt class="py-name">flush_delay</tt><tt class="py-op">,</tt> <tt class="py-name">func_args</tt><tt class="py-op">,</tt> <tt class="py-name">func_kwargs</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">,</tt>  </tt>
<a name="L723"></a><tt class="py-lineno">723</tt>  <tt class="py-line">            <tt class="py-name">ll_scale</tt><tt class="py-op">,</tt> <tt class="py-name">output_stream</tt><tt class="py-op">)</tt> </tt>
<a name="L724"></a><tt class="py-lineno">724</tt>  <tt class="py-line"> </tt>
<a name="L725"></a><tt class="py-lineno">725</tt>  <tt class="py-line">    <tt class="py-comment"># Make bounds list. For this method it needs to be in terms of log params.</tt> </tt>
<a name="L726"></a><tt class="py-lineno">726</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">lower_bound</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L727"></a><tt class="py-lineno">727</tt>  <tt class="py-line">        <tt class="py-name">lower_bound</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">None</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt> </tt>
<a name="L728"></a><tt class="py-lineno">728</tt>  <tt class="py-line">    <tt class="py-name">lower_bound</tt> <tt class="py-op">=</tt> <tt id="link-64" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-64', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">lower_bound</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L729"></a><tt class="py-lineno">729</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">upper_bound</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L730"></a><tt class="py-lineno">730</tt>  <tt class="py-line">        <tt class="py-name">upper_bound</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">None</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt> </tt>
<a name="L731"></a><tt class="py-lineno">731</tt>  <tt class="py-line">    <tt class="py-name">upper_bound</tt> <tt class="py-op">=</tt> <tt id="link-65" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-65', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">upper_bound</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L732"></a><tt class="py-lineno">732</tt>  <tt class="py-line">    <tt class="py-name">bounds</tt> <tt class="py-op">=</tt> <tt class="py-name">list</tt><tt class="py-op">(</tt><tt class="py-name">zip</tt><tt class="py-op">(</tt><tt class="py-name">lower_bound</tt><tt class="py-op">,</tt><tt class="py-name">upper_bound</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L733"></a><tt class="py-lineno">733</tt>  <tt class="py-line"> </tt>
<a name="L734"></a><tt class="py-lineno">734</tt>  <tt class="py-line">    <tt class="py-name">p0</tt> <tt class="py-op">=</tt> <tt id="link-66" class="py-name"><a title="dadi.Inference._project_params_down" class="py-name" href="#" onclick="return doclink('link-66', '_project_params_down', 'link-25');">_project_params_down</a></tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L735"></a><tt class="py-lineno">735</tt>  <tt class="py-line"> </tt>
<a name="L736"></a><tt class="py-lineno">736</tt>  <tt class="py-line">    <tt class="py-name">outputs</tt> <tt class="py-op">=</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt id="link-67" class="py-name"><a title="dadi.Inference.optimize" class="py-name" href="#" onclick="return doclink('link-67', 'optimize', 'link-4');">optimize</a></tt><tt class="py-op">.</tt><tt class="py-name">fmin_l_bfgs_b</tt><tt class="py-op">(</tt><tt id="link-68" class="py-name"><a title="dadi.Inference._object_func" class="py-name" href="#" onclick="return doclink('link-68', '_object_func', 'link-24');">_object_func</a></tt><tt class="py-op">,</tt>  </tt>
<a name="L737"></a><tt class="py-lineno">737</tt>  <tt class="py-line">                                           <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">log</tt><tt class="py-op">(</tt><tt class="py-name">p0</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">bounds</tt><tt class="py-op">=</tt><tt class="py-name">bounds</tt><tt class="py-op">,</tt> </tt>
<a name="L738"></a><tt class="py-lineno">738</tt>  <tt class="py-line">                                           <tt class="py-name">epsilon</tt><tt class="py-op">=</tt><tt class="py-name">epsilon</tt><tt class="py-op">,</tt> <tt class="py-name">args</tt><tt class="py-op">=</tt><tt class="py-name">args</tt><tt class="py-op">,</tt> </tt>
<a name="L739"></a><tt class="py-lineno">739</tt>  <tt class="py-line">                                           <tt class="py-name">iprint</tt><tt class="py-op">=</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-name">pgtol</tt><tt class="py-op">=</tt><tt class="py-name">pgtol</tt><tt class="py-op">,</tt> </tt>
<a name="L740"></a><tt class="py-lineno">740</tt>  <tt class="py-line">                                           <tt class="py-name">maxfun</tt><tt class="py-op">=</tt><tt class="py-name">maxiter</tt><tt class="py-op">,</tt> <tt class="py-name">approx_grad</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">)</tt> </tt>
<a name="L741"></a><tt class="py-lineno">741</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">info_dict</tt> <tt class="py-op">=</tt> <tt class="py-name">outputs</tt> </tt>
<a name="L742"></a><tt class="py-lineno">742</tt>  <tt class="py-line"> </tt>
<a name="L743"></a><tt class="py-lineno">743</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt> <tt class="py-op">=</tt> <tt id="link-69" class="py-name"><a title="dadi.Inference._project_params_up" class="py-name" href="#" onclick="return doclink('link-69', '_project_params_up', 'link-10');">_project_params_up</a></tt><tt class="py-op">(</tt><tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L744"></a><tt class="py-lineno">744</tt>  <tt class="py-line"> </tt>
<a name="L745"></a><tt class="py-lineno">745</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L746"></a><tt class="py-lineno">746</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt><tt class="py-op">.</tt><tt class="py-name">close</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L747"></a><tt class="py-lineno">747</tt>  <tt class="py-line"> </tt>
<a name="L748"></a><tt class="py-lineno">748</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L749"></a><tt class="py-lineno">749</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt> </tt>
<a name="L750"></a><tt class="py-lineno">750</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L751"></a><tt class="py-lineno">751</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">info_dict</tt> </tt>
</div><a name="L752"></a><tt class="py-lineno">752</tt>  <tt class="py-line"> </tt>
<a name="_project_params_down"></a><div id="_project_params_down-def"><a name="L753"></a><tt class="py-lineno">753</tt> <a class="py-toggle" href="#" id="_project_params_down-toggle" onclick="return toggle('_project_params_down');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#_project_params_down">_project_params_down</a><tt class="py-op">(</tt><tt class="py-param">pin</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_project_params_down-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_project_params_down-expanded"><a name="L754"></a><tt class="py-lineno">754</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L755"></a><tt class="py-lineno">755</tt>  <tt class="py-line"><tt class="py-docstring">    Eliminate fixed parameters from pin.</tt> </tt>
<a name="L756"></a><tt class="py-lineno">756</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L757"></a><tt class="py-lineno">757</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">fixed_params</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L758"></a><tt class="py-lineno">758</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">pin</tt> </tt>
<a name="L759"></a><tt class="py-lineno">759</tt>  <tt class="py-line"> </tt>
<a name="L760"></a><tt class="py-lineno">760</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">pin</tt><tt class="py-op">)</tt> <tt class="py-op">!=</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">fixed_params</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L761"></a><tt class="py-lineno">761</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'fixed_params list must have same length as input '</tt> </tt>
<a name="L762"></a><tt class="py-lineno">762</tt>  <tt class="py-line">                         <tt class="py-string">'parameter array.'</tt><tt class="py-op">)</tt> </tt>
<a name="L763"></a><tt class="py-lineno">763</tt>  <tt class="py-line"> </tt>
<a name="L764"></a><tt class="py-lineno">764</tt>  <tt class="py-line">    <tt class="py-name">pout</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L765"></a><tt class="py-lineno">765</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">ii</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-name">curr_val</tt><tt class="py-op">,</tt><tt class="py-name">fixed_val</tt><tt class="py-op">)</tt> <tt class="py-keyword">in</tt> <tt class="py-name">enumerate</tt><tt class="py-op">(</tt><tt class="py-name">zip</tt><tt class="py-op">(</tt><tt class="py-name">pin</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L766"></a><tt class="py-lineno">766</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">fixed_val</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L767"></a><tt class="py-lineno">767</tt>  <tt class="py-line">            <tt class="py-name">pout</tt><tt class="py-op">.</tt><tt class="py-name">append</tt><tt class="py-op">(</tt><tt class="py-name">curr_val</tt><tt class="py-op">)</tt> </tt>
<a name="L768"></a><tt class="py-lineno">768</tt>  <tt class="py-line"> </tt>
<a name="L769"></a><tt class="py-lineno">769</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">array</tt><tt class="py-op">(</tt><tt class="py-name">pout</tt><tt class="py-op">)</tt> </tt>
</div><a name="L770"></a><tt class="py-lineno">770</tt>  <tt class="py-line"> </tt>
<a name="_project_params_up"></a><div id="_project_params_up-def"><a name="L771"></a><tt class="py-lineno">771</tt> <a class="py-toggle" href="#" id="_project_params_up-toggle" onclick="return toggle('_project_params_up');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#_project_params_up">_project_params_up</a><tt class="py-op">(</tt><tt class="py-param">pin</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_project_params_up-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_project_params_up-expanded"><a name="L772"></a><tt class="py-lineno">772</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L773"></a><tt class="py-lineno">773</tt>  <tt class="py-line"><tt class="py-docstring">    Fold fixed parameters into pin.</tt> </tt>
<a name="L774"></a><tt class="py-lineno">774</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L775"></a><tt class="py-lineno">775</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">fixed_params</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L776"></a><tt class="py-lineno">776</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">pin</tt> </tt>
<a name="L777"></a><tt class="py-lineno">777</tt>  <tt class="py-line"> </tt>
<a name="L778"></a><tt class="py-lineno">778</tt>  <tt class="py-line">    <tt class="py-name">pout</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">fixed_params</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L779"></a><tt class="py-lineno">779</tt>  <tt class="py-line">    <tt class="py-name">orig_ii</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L780"></a><tt class="py-lineno">780</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">out_ii</tt><tt class="py-op">,</tt> <tt class="py-name">val</tt> <tt class="py-keyword">in</tt> <tt class="py-name">enumerate</tt><tt class="py-op">(</tt><tt class="py-name">fixed_params</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L781"></a><tt class="py-lineno">781</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">val</tt> <tt class="py-keyword">is</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L782"></a><tt class="py-lineno">782</tt>  <tt class="py-line">            <tt class="py-name">pout</tt><tt class="py-op">[</tt><tt class="py-name">out_ii</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">pin</tt><tt class="py-op">[</tt><tt class="py-name">orig_ii</tt><tt class="py-op">]</tt> </tt>
<a name="L783"></a><tt class="py-lineno">783</tt>  <tt class="py-line">            <tt class="py-name">orig_ii</tt> <tt class="py-op">+=</tt> <tt class="py-number">1</tt> </tt>
<a name="L784"></a><tt class="py-lineno">784</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L785"></a><tt class="py-lineno">785</tt>  <tt class="py-line">            <tt class="py-name">pout</tt><tt class="py-op">[</tt><tt class="py-name">out_ii</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">[</tt><tt class="py-name">out_ii</tt><tt class="py-op">]</tt> </tt>
<a name="L786"></a><tt class="py-lineno">786</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">pout</tt> </tt>
</div><a name="L787"></a><tt class="py-lineno">787</tt>  <tt class="py-line"> </tt>
<a name="L788"></a><tt class="py-lineno">788</tt>  <tt class="py-line"><tt id="link-70" class="py-name" targets="Variable dadi.Inference.index_exp=dadi.Inference-module.html#index_exp"><a title="dadi.Inference.index_exp" class="py-name" href="#" onclick="return doclink('link-70', 'index_exp', 'link-70');">index_exp</a></tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt id="link-71" class="py-name"><a title="dadi.Inference.index_exp" class="py-name" href="#" onclick="return doclink('link-71', 'index_exp', 'link-70');">index_exp</a></tt> </tt>
<a name="optimize_grid"></a><div id="optimize_grid-def"><a name="L789"></a><tt class="py-lineno">789</tt> <a class="py-toggle" href="#" id="optimize_grid-toggle" onclick="return toggle('optimize_grid');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Inference-module.html#optimize_grid">optimize_grid</a><tt class="py-op">(</tt><tt class="py-param">data</tt><tt class="py-op">,</tt> <tt class="py-param">model_func</tt><tt class="py-op">,</tt> <tt class="py-param">pts</tt><tt class="py-op">,</tt> <tt class="py-param">grid</tt><tt class="py-op">,</tt> </tt>
<a name="L790"></a><tt class="py-lineno">790</tt>  <tt class="py-line">                  <tt class="py-param">verbose</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">flush_delay</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> </tt>
<a name="L791"></a><tt class="py-lineno">791</tt>  <tt class="py-line">                  <tt class="py-param">multinom</tt><tt class="py-op">=</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-param">full_output</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L792"></a><tt class="py-lineno">792</tt>  <tt class="py-line">                  <tt class="py-param">func_args</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-param">func_kwargs</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">,</tt> <tt class="py-param">fixed_params</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">,</tt> </tt>
<a name="L793"></a><tt class="py-lineno">793</tt>  <tt class="py-line">                  <tt class="py-param">output_file</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="optimize_grid-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="optimize_grid-expanded"><a name="L794"></a><tt class="py-lineno">794</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L795"></a><tt class="py-lineno">795</tt>  <tt class="py-line"><tt class="py-docstring">    Optimize params to fit model to data using brute force search over a grid.</tt> </tt>
<a name="L796"></a><tt class="py-lineno">796</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L797"></a><tt class="py-lineno">797</tt>  <tt class="py-line"><tt class="py-docstring">    data: Spectrum with data.</tt> </tt>
<a name="L798"></a><tt class="py-lineno">798</tt>  <tt class="py-line"><tt class="py-docstring">    model_func: Function to evaluate model spectrum. Should take arguments</tt> </tt>
<a name="L799"></a><tt class="py-lineno">799</tt>  <tt class="py-line"><tt class="py-docstring">                (params, (n1,n2...), pts)</tt> </tt>
<a name="L800"></a><tt class="py-lineno">800</tt>  <tt class="py-line"><tt class="py-docstring">    pts: Grid points list for evaluating likelihoods</tt> </tt>
<a name="L801"></a><tt class="py-lineno">801</tt>  <tt class="py-line"><tt class="py-docstring">    grid: Grid of parameter values over which to evaluate likelihood. See</tt> </tt>
<a name="L802"></a><tt class="py-lineno">802</tt>  <tt class="py-line"><tt class="py-docstring">          below for specification instructions.</tt> </tt>
<a name="L803"></a><tt class="py-lineno">803</tt>  <tt class="py-line"><tt class="py-docstring">    verbose: If &gt; 0, print optimization status every &lt;verbose&gt; steps.</tt> </tt>
<a name="L804"></a><tt class="py-lineno">804</tt>  <tt class="py-line"><tt class="py-docstring">    output_file: Stream verbose output into this filename. If None, stream to</tt> </tt>
<a name="L805"></a><tt class="py-lineno">805</tt>  <tt class="py-line"><tt class="py-docstring">                 standard out.</tt> </tt>
<a name="L806"></a><tt class="py-lineno">806</tt>  <tt class="py-line"><tt class="py-docstring">    flush_delay: Standard output will be flushed once every &lt;flush_delay&gt;</tt> </tt>
<a name="L807"></a><tt class="py-lineno">807</tt>  <tt class="py-line"><tt class="py-docstring">                 minutes. This is useful to avoid overloading I/O on clusters.</tt> </tt>
<a name="L808"></a><tt class="py-lineno">808</tt>  <tt class="py-line"><tt class="py-docstring">    multinom: If True, do a multinomial fit where model is optimially scaled to</tt> </tt>
<a name="L809"></a><tt class="py-lineno">809</tt>  <tt class="py-line"><tt class="py-docstring">              data at each step. If False, assume theta is a parameter and do</tt> </tt>
<a name="L810"></a><tt class="py-lineno">810</tt>  <tt class="py-line"><tt class="py-docstring">              no scaling.</tt> </tt>
<a name="L811"></a><tt class="py-lineno">811</tt>  <tt class="py-line"><tt class="py-docstring">    full_output: If True, return popt, llopt, grid, llout, thetas. Here popt is</tt> </tt>
<a name="L812"></a><tt class="py-lineno">812</tt>  <tt class="py-line"><tt class="py-docstring">                 the best parameter set found and llopt is the corresponding</tt> </tt>
<a name="L813"></a><tt class="py-lineno">813</tt>  <tt class="py-line"><tt class="py-docstring">                 (composite) log-likelihood. grid is the array of parameter</tt> </tt>
<a name="L814"></a><tt class="py-lineno">814</tt>  <tt class="py-line"><tt class="py-docstring">                 values tried, llout is the corresponding log-likelihoods, and</tt> </tt>
<a name="L815"></a><tt class="py-lineno">815</tt>  <tt class="py-line"><tt class="py-docstring">                 thetas is the corresponding thetas. Note that the grid includes</tt> </tt>
<a name="L816"></a><tt class="py-lineno">816</tt>  <tt class="py-line"><tt class="py-docstring">                 only the parameters optimized over, and that the order of</tt> </tt>
<a name="L817"></a><tt class="py-lineno">817</tt>  <tt class="py-line"><tt class="py-docstring">                 indices is such that grid[:,0,2] would be a set of parameters</tt> </tt>
<a name="L818"></a><tt class="py-lineno">818</tt>  <tt class="py-line"><tt class="py-docstring">                 if two parameters were optimized over. (Note the : in the</tt> </tt>
<a name="L819"></a><tt class="py-lineno">819</tt>  <tt class="py-line"><tt class="py-docstring">                 first index.)</tt> </tt>
<a name="L820"></a><tt class="py-lineno">820</tt>  <tt class="py-line"><tt class="py-docstring">    func_args: Additional arguments to model_func. It is assumed that </tt> </tt>
<a name="L821"></a><tt class="py-lineno">821</tt>  <tt class="py-line"><tt class="py-docstring">               model_func's first argument is an array of parameters to</tt> </tt>
<a name="L822"></a><tt class="py-lineno">822</tt>  <tt class="py-line"><tt class="py-docstring">               optimize, that its second argument is an array of sample sizes</tt> </tt>
<a name="L823"></a><tt class="py-lineno">823</tt>  <tt class="py-line"><tt class="py-docstring">               for the sfs, and that its last argument is the list of grid</tt> </tt>
<a name="L824"></a><tt class="py-lineno">824</tt>  <tt class="py-line"><tt class="py-docstring">               points to use in evaluation.</tt> </tt>
<a name="L825"></a><tt class="py-lineno">825</tt>  <tt class="py-line"><tt class="py-docstring">    func_kwargs: Additional keyword arguments to model_func.</tt> </tt>
<a name="L826"></a><tt class="py-lineno">826</tt>  <tt class="py-line"><tt class="py-docstring">    fixed_params: If not None, should be a list used to fix model parameters at</tt> </tt>
<a name="L827"></a><tt class="py-lineno">827</tt>  <tt class="py-line"><tt class="py-docstring">                  particular values. For example, if the model parameters</tt> </tt>
<a name="L828"></a><tt class="py-lineno">828</tt>  <tt class="py-line"><tt class="py-docstring">                  are (nu1,nu2,T,m), then fixed_params = [0.5,None,None,2]</tt> </tt>
<a name="L829"></a><tt class="py-lineno">829</tt>  <tt class="py-line"><tt class="py-docstring">                  will hold nu1=0.5 and m=2. The optimizer will only change </tt> </tt>
<a name="L830"></a><tt class="py-lineno">830</tt>  <tt class="py-line"><tt class="py-docstring">                  T and m. Note that the bounds lists must include all</tt> </tt>
<a name="L831"></a><tt class="py-lineno">831</tt>  <tt class="py-line"><tt class="py-docstring">                  parameters. Optimization will fail if the fixed values</tt> </tt>
<a name="L832"></a><tt class="py-lineno">832</tt>  <tt class="py-line"><tt class="py-docstring">                  lie outside their bounds. A full-length p0 should be passed</tt> </tt>
<a name="L833"></a><tt class="py-lineno">833</tt>  <tt class="py-line"><tt class="py-docstring">                  in; values corresponding to fixed parameters are ignored.</tt> </tt>
<a name="L834"></a><tt class="py-lineno">834</tt>  <tt class="py-line"><tt class="py-docstring">    (See help(dadi.Inference.optimize_log for examples of func_args and </tt> </tt>
<a name="L835"></a><tt class="py-lineno">835</tt>  <tt class="py-line"><tt class="py-docstring">     fixed_params usage.)</tt> </tt>
<a name="L836"></a><tt class="py-lineno">836</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L837"></a><tt class="py-lineno">837</tt>  <tt class="py-line"><tt class="py-docstring">    Search grids are specified using a dadi.Inference.index_exp object (which</tt> </tt>
<a name="L838"></a><tt class="py-lineno">838</tt>  <tt class="py-line"><tt class="py-docstring">    is an alias for numpy.index_exp). The grid is specified by passing a range</tt> </tt>
<a name="L839"></a><tt class="py-lineno">839</tt>  <tt class="py-line"><tt class="py-docstring">    of values for each parameter. For example, index_exp[0:1.1:0.3,</tt> </tt>
<a name="L840"></a><tt class="py-lineno">840</tt>  <tt class="py-line"><tt class="py-docstring">    0.7:0.9:11j] will search over parameter 1 with values 0,0.3,0.6,0.9 and</tt> </tt>
<a name="L841"></a><tt class="py-lineno">841</tt>  <tt class="py-line"><tt class="py-docstring">    over parameter 2 with 11 points between 0.7 and 0.9 (inclusive). (Notice</tt> </tt>
<a name="L842"></a><tt class="py-lineno">842</tt>  <tt class="py-line"><tt class="py-docstring">    the 11j in the second parameter range specification.) Note that the grid</tt> </tt>
<a name="L843"></a><tt class="py-lineno">843</tt>  <tt class="py-line"><tt class="py-docstring">    list should include only parameters that are optimized over, not fixed</tt> </tt>
<a name="L844"></a><tt class="py-lineno">844</tt>  <tt class="py-line"><tt class="py-docstring">    parameter values.</tt> </tt>
<a name="L845"></a><tt class="py-lineno">845</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L846"></a><tt class="py-lineno">846</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L847"></a><tt class="py-lineno">847</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">file</tt><tt class="py-op">(</tt><tt class="py-name">output_file</tt><tt class="py-op">,</tt> <tt class="py-string">'w'</tt><tt class="py-op">)</tt> </tt>
<a name="L848"></a><tt class="py-lineno">848</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L849"></a><tt class="py-lineno">849</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt> <tt class="py-op">=</tt> <tt class="py-name">sys</tt><tt class="py-op">.</tt><tt class="py-name">stdout</tt> </tt>
<a name="L850"></a><tt class="py-lineno">850</tt>  <tt class="py-line"> </tt>
<a name="L851"></a><tt class="py-lineno">851</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">data</tt><tt class="py-op">,</tt> <tt class="py-name">model_func</tt><tt class="py-op">,</tt> <tt class="py-name">pts</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">verbose</tt><tt class="py-op">,</tt> </tt>
<a name="L852"></a><tt class="py-lineno">852</tt>  <tt class="py-line">            <tt class="py-name">multinom</tt><tt class="py-op">,</tt> <tt class="py-name">flush_delay</tt><tt class="py-op">,</tt> <tt class="py-name">func_args</tt><tt class="py-op">,</tt> <tt class="py-name">func_kwargs</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">,</tt> <tt class="py-number">1.0</tt><tt class="py-op">,</tt> </tt>
<a name="L853"></a><tt class="py-lineno">853</tt>  <tt class="py-line">            <tt class="py-name">output_stream</tt><tt class="py-op">,</tt> <tt class="py-name">full_output</tt><tt class="py-op">)</tt> </tt>
<a name="L854"></a><tt class="py-lineno">854</tt>  <tt class="py-line"> </tt>
<a name="L855"></a><tt class="py-lineno">855</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L856"></a><tt class="py-lineno">856</tt>  <tt class="py-line">        <tt class="py-keyword">global</tt> <tt id="link-72" class="py-name"><a title="dadi.Inference._theta_store" class="py-name" href="#" onclick="return doclink('link-72', '_theta_store', 'link-5');">_theta_store</a></tt> </tt>
<a name="L857"></a><tt class="py-lineno">857</tt>  <tt class="py-line">        <tt id="link-73" class="py-name"><a title="dadi.Inference._theta_store" class="py-name" href="#" onclick="return doclink('link-73', '_theta_store', 'link-5');">_theta_store</a></tt> <tt class="py-op">=</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt> </tt>
<a name="L858"></a><tt class="py-lineno">858</tt>  <tt class="py-line"> </tt>
<a name="L859"></a><tt class="py-lineno">859</tt>  <tt class="py-line">    <tt class="py-name">outputs</tt> <tt class="py-op">=</tt> <tt class="py-name">scipy</tt><tt class="py-op">.</tt><tt id="link-74" class="py-name"><a title="dadi.Inference.optimize" class="py-name" href="#" onclick="return doclink('link-74', 'optimize', 'link-4');">optimize</a></tt><tt class="py-op">.</tt><tt class="py-name">brute</tt><tt class="py-op">(</tt><tt id="link-75" class="py-name"><a title="dadi.Inference._object_func" class="py-name" href="#" onclick="return doclink('link-75', '_object_func', 'link-24');">_object_func</a></tt><tt class="py-op">,</tt> <tt class="py-name">ranges</tt><tt class="py-op">=</tt><tt class="py-name">grid</tt><tt class="py-op">,</tt> </tt>
<a name="L860"></a><tt class="py-lineno">860</tt>  <tt class="py-line">                                   <tt class="py-name">args</tt><tt class="py-op">=</tt><tt class="py-name">args</tt><tt class="py-op">,</tt> <tt class="py-name">full_output</tt><tt class="py-op">=</tt><tt class="py-name">full_output</tt><tt class="py-op">,</tt> </tt>
<a name="L861"></a><tt class="py-lineno">861</tt>  <tt class="py-line">                                   <tt class="py-name">finish</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">)</tt> </tt>
<a name="L862"></a><tt class="py-lineno">862</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L863"></a><tt class="py-lineno">863</tt>  <tt class="py-line">        <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">grid</tt><tt class="py-op">,</tt> <tt class="py-name">fout</tt> <tt class="py-op">=</tt> <tt class="py-name">outputs</tt> </tt>
<a name="L864"></a><tt class="py-lineno">864</tt>  <tt class="py-line">        <tt class="py-comment"># Thetas are stored as a dictionary, because we can't guarantee</tt> </tt>
<a name="L865"></a><tt class="py-lineno">865</tt>  <tt class="py-line">        <tt class="py-comment"># iteration order in brute(). So we have to iterate back over them</tt> </tt>
<a name="L866"></a><tt class="py-lineno">866</tt>  <tt class="py-line">        <tt class="py-comment"># to produce the proper order to return.</tt> </tt>
<a name="L867"></a><tt class="py-lineno">867</tt>  <tt class="py-line">        <tt class="py-name">thetas</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">fout</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L868"></a><tt class="py-lineno">868</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">indices</tt><tt class="py-op">,</tt> <tt class="py-name">temp</tt> <tt class="py-keyword">in</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">ndenumerate</tt><tt class="py-op">(</tt><tt class="py-name">fout</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L869"></a><tt class="py-lineno">869</tt>  <tt class="py-line">            <tt class="py-comment"># This is awkward, because we need to access grid[:,indices]</tt> </tt>
<a name="L870"></a><tt class="py-lineno">870</tt>  <tt class="py-line">            <tt class="py-name">grid_indices</tt> <tt class="py-op">=</tt> <tt class="py-name">tuple</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">slice</tt><tt class="py-op">(</tt><tt class="py-name">None</tt><tt class="py-op">,</tt><tt class="py-name">None</tt><tt class="py-op">,</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">list</tt><tt class="py-op">(</tt><tt class="py-name">indices</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L871"></a><tt class="py-lineno">871</tt>  <tt class="py-line">            <tt class="py-name">thetas</tt><tt class="py-op">[</tt><tt class="py-name">indices</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt id="link-76" class="py-name"><a title="dadi.Inference._theta_store" class="py-name" href="#" onclick="return doclink('link-76', '_theta_store', 'link-5');">_theta_store</a></tt><tt class="py-op">[</tt><tt class="py-name">tuple</tt><tt class="py-op">(</tt><tt class="py-name">grid</tt><tt class="py-op">[</tt><tt class="py-name">grid_indices</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L872"></a><tt class="py-lineno">872</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L873"></a><tt class="py-lineno">873</tt>  <tt class="py-line">        <tt class="py-name">xopt</tt> <tt class="py-op">=</tt> <tt class="py-name">outputs</tt> </tt>
<a name="L874"></a><tt class="py-lineno">874</tt>  <tt class="py-line">    <tt class="py-name">xopt</tt> <tt class="py-op">=</tt> <tt id="link-77" class="py-name"><a title="dadi.Inference._project_params_up" class="py-name" href="#" onclick="return doclink('link-77', '_project_params_up', 'link-10');">_project_params_up</a></tt><tt class="py-op">(</tt><tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fixed_params</tt><tt class="py-op">)</tt> </tt>
<a name="L875"></a><tt class="py-lineno">875</tt>  <tt class="py-line"> </tt>
<a name="L876"></a><tt class="py-lineno">876</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">output_file</tt><tt class="py-op">:</tt> </tt>
<a name="L877"></a><tt class="py-lineno">877</tt>  <tt class="py-line">        <tt class="py-name">output_stream</tt><tt class="py-op">.</tt><tt class="py-name">close</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L878"></a><tt class="py-lineno">878</tt>  <tt class="py-line"> </tt>
<a name="L879"></a><tt class="py-lineno">879</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">full_output</tt><tt class="py-op">:</tt> </tt>
<a name="L880"></a><tt class="py-lineno">880</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt> </tt>
<a name="L881"></a><tt class="py-lineno">881</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L882"></a><tt class="py-lineno">882</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">xopt</tt><tt class="py-op">,</tt> <tt class="py-name">fopt</tt><tt class="py-op">,</tt> <tt class="py-name">grid</tt><tt class="py-op">,</tt> <tt class="py-name">fout</tt><tt class="py-op">,</tt> <tt class="py-name">thetas</tt> </tt>
</div><a name="L883"></a><tt class="py-lineno">883</tt>  <tt class="py-line"> </tt><script type="text/javascript">
<!--
expandto(location.href);
// -->
</script>
</pre>
<br />
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
       bgcolor="#a0c0ff" cellspacing="0">
  <tr valign="middle">

  <!-- Tree link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="module-tree.html">Trees</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Index link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="identifier-index.html">Indices</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Help link -->
      <th>&nbsp;&nbsp;&nbsp;<a
        href="help.html">Help</a>&nbsp;&nbsp;&nbsp;</th>

  <!-- Project homepage -->
      <th class="navbar" align="right" width="100%">
        <table border="0" cellpadding="0" cellspacing="0">
          <tr><th class="navbar" align="center"
            ><a class="navbar" target="_top" href="http://dadi.googlecode.com">dadi</a></th>
          </tr></table></th>
  </tr>
</table>
<table border="0" cellpadding="0" cellspacing="0" width="100%%">
  <tr>
    <td align="left" class="footer">
    <a href="epydoc-log.html">Generated by Epydoc
    3.0.1 on Fri Dec 14 15:16:34 2012</a>
    </td>
    <td align="right" class="footer">
      <a target="mainFrame" href="http://epydoc.sourceforge.net"
        >http://epydoc.sourceforge.net</a>
    </td>
  </tr>
</table>

<script type="text/javascript">
  <!--
  // Private objects are initially displayed (because if
  // javascript is turned off then we want them to be
  // visible); but by default, we want to hide them.  So hide
  // them unless we have a cookie that says to show them.
  checkCookie();
  // -->
</script>
</body>
</html>
